Business Statistics Quiz: Choosing Statistical Methods
20 questions · exam conditions
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Choosing Statistical MethodsQuestion 1 of 20

A quality control manager at a bottling plant wants to ensure two machines (Machine A and Machine B) are filling bottles with the same level of consistency. The target fill volume is 500 mL. The manager is less concerned with the average fill volume and more concerned with whether one machine has significantly more variability in its fills than the other. Which statistical test should be used to address this specific concern?

An independent two-sample t-test to determine if the mean fill volume is different between the two machines.
A paired t-test to compare the fill volumes from Machine A and Machine B for each production run.
An F-test for the equality of two variances to compare the sample variances of fill volumes from each machine.
A chi-squared test to analyze the distribution of fill volumes against a normal distribution for each machine.
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Business Statistics Quiz

Business Statistics Quiz: Choosing Statistical Methods

Practice Choosing Statistical Methods in Business Statistics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Choosing Statistical Methods, giving you a quick way to practice the rules, question types, and explanations that matter most for Business Statistics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A quality control manager at a bottling plant wants to ensure two machines (Machine A and Machine B) are filling bottles with the same level of consistency. The target fill volume is 500 mL. The manager is less concerned with the average fill volume and more concerned with whether one machine has significantly more variability in its fills than the other. Which statistical test should be used to address this specific concern?

  1. An independent two-sample t-test to determine if the mean fill volume is different between the two machines.
  2. A paired t-test to compare the fill volumes from Machine A and Machine B for each production run.
  3. An F-test for the equality of two variances to compare the sample variances of fill volumes from each machine. (correct answer)
  4. A chi-squared test to analyze the distribution of fill volumes against a normal distribution for each machine.
Explanation: The business question is explicitly about comparing the variability (consistency) of two independent groups, not their means. The F-test for equality of variances is the appropriate inferential test for comparing the variances (or standard deviations) of two populations, assuming the data is approximately normally distributed.

Question 2

An operations manager wants to quantify the strength and direction of the linear relationship between the ambient temperature in a factory and the number of defects per hour produced by a sensitive machine. Data on both variables is collected over 100 different shifts. Which statistic would be most appropriate to calculate for this purpose?

  1. The Pearson correlation coefficient (r) between temperature and number of defects. (correct answer)
  2. The coefficient of determination (R-squared) from a regression analysis.
  3. A simple linear regression model to predict defects from temperature.
  4. The covariance between temperature and the number of defects.
Explanation: When you encounter questions about measuring the "strength and direction" of a linear relationship between two variables, you're dealing with correlation analysis. The key phrase here is that the manager wants to quantify both how strong the relationship is AND whether it's positive or negative. The Pearson correlation coefficient (r) is specifically designed for this purpose. It measures both the strength (ranging from 0 to 1 in absolute value) and direction (positive or negative sign) of linear relationships between two continuous variables. Since temperature and defect counts are both continuous variables, and the manager wants to understand their linear association, option A gives you exactly what's needed in a single, interpretable statistic. Let's examine why the other options miss the mark. Option B, the coefficient of determination (R-squared), only tells you the strength of the relationship (as a proportion of variance explained) but doesn't indicate direction - you lose the crucial information about whether higher temperatures increase or decrease defects. Option C, creating a regression model, goes beyond what's asked; while useful for prediction, it's overkill when you simply want to quantify the relationship's strength and direction. Option D, covariance, does capture direction, but it's not standardized, making it difficult to interpret the strength of the relationship since it depends on the units of measurement. Remember this pattern: when a question asks specifically for "strength AND direction" of a linear relationship, the Pearson correlation coefficient is almost always your answer. It's the only measure that gives you both pieces of information in one easily interpretable number.

Question 3

A quality improvement team wants to determine if a new training program affects employee error rates. They have error rate data for 45 employees before implementing the training and error rate data for a different group of 38 employees after implementing the training. The two groups were not matched, and employees in each group are independent.

What is the most appropriate statistical test to determine if the training program significantly changed employee error rates?

  1. Paired t-test comparing before and after error rates since we're measuring the same outcome variable in both conditions
  2. One-way ANOVA with training status as the factor and error rate as the dependent variable to test for differences
  3. Two-sample t-test comparing mean error rates between the before-training and after-training groups with independent samples (correct answer)
  4. Chi-square test comparing the proportion of employees with high error rates before and after training implementation
Explanation: When you encounter questions about comparing groups in business statistics, the key decision point is whether you're dealing with paired or independent samples, and what type of data you're analyzing. The correct approach here is C) Two-sample t-test comparing mean error rates between the before-training and after-training groups with independent samples. This scenario involves two completely separate groups of employees (45 before, 38 after) with no matching or pairing between individuals. Since error rates are continuous numerical data and you want to compare the means between two independent groups, a two-sample t-test is the appropriate choice. A is wrong because a paired t-test requires the same subjects measured twice or matched pairs. Here, you have entirely different employees in each group, making pairing impossible. B is technically possible but unnecessarily complex. While one-way ANOVA can compare two groups, it's designed for comparing three or more groups. A t-test is the simpler, more direct approach for two-group comparisons and is preferred when applicable. D is incorrect because you're dealing with actual error rate values (continuous data), not categorical data about whether employees have "high" or "low" error rates. Chi-square tests are for categorical variables, not continuous measurements like error rates. Study tip: Always identify three things first: (1) Are your samples paired or independent? (2) How many groups are you comparing? (3) Is your outcome variable continuous or categorical? This framework will guide you to the right statistical test every time.

Question 4

An online retailer wants to understand the relationship between the average number of items a customer places in their shopping cart and their type of membership ('Premium', 'Standard', 'Guest'). The data is collected from 1,000 recent transactions. The goal is to determine if the mean number of items in the cart differs significantly across these three distinct membership levels. Which statistical method should the retailer use?

  1. Chi-squared test of independence to see if membership type is related to purchasing behavior.
  2. One-way Analysis of Variance (ANOVA) to compare the mean number of items among the three membership groups. (correct answer)
  3. Pearson correlation coefficient to measure the strength of the relationship between membership and items.
  4. Multiple regression to predict the number of items in the cart based on membership level and other factors.
Explanation: The problem involves comparing the mean of a continuous variable (number of items) across three or more independent categorical groups (membership levels). This is the classic application for a one-way ANOVA.

Question 5

A retail chain manager wants to forecast monthly sales for the next quarter based on historical monthly sales data from the past 3 years. The data shows clear seasonal patterns with higher sales in November and December, and the manager needs point estimates for planning inventory and staffing.

Which analytical method would be most appropriate for generating the quarterly sales forecasts needed for business planning?

  1. Time series analysis with seasonal decomposition to model trend and seasonal components for forecasting future periods (correct answer)
  2. Multiple regression using month number and year as predictor variables to forecast sales for upcoming months
  3. One-sample t-test to determine if historical monthly sales significantly differ from a target sales level for planning
  4. ANOVA comparing mean sales across different months to identify which months have significantly higher sales patterns
Explanation: Time series analysis with seasonal decomposition is most appropriate because the data has clear seasonal patterns and temporal dependencies, and the goal is forecasting future periods. This method specifically handles trend and seasonal components for prediction. Option B (regression) doesn't adequately capture seasonal patterns or temporal dependencies inherent in time series data. Option C (t-test) tests against a target value but doesn't provide forecasts. Option D (ANOVA) identifies seasonal differences but doesn't provide forecasting capability or account for temporal trends.

Question 6

A business analyst is studying factors that influence customer purchase amounts at an e-commerce site. They have data on customer age, annual income, number of previous purchases, and whether the customer used a mobile device (yes/no) for a sample of 200 customers. The goal is to predict purchase amount based on these variables.

Which analytical approach would be most appropriate for determining how well these variables collectively predict customer purchase amounts?

  1. Multiple correlation analysis to examine the strength of linear relationships between all predictor variables and purchase amount
  2. Logistic regression with customer characteristics predicting high versus low purchase amount categories as the outcome variable
  3. Series of simple linear regressions, one for each predictor variable, to determine individual effects on purchase amount
  4. Multiple linear regression with purchase amount as dependent variable and all customer characteristics as independent variables (correct answer)
Explanation: When you encounter a question about predicting a continuous outcome variable using multiple predictor variables, you're dealing with regression analysis. The key is matching the analytical method to both your outcome variable type and your research goal. Multiple linear regression (D) is the correct approach here because you want to predict purchase amount—a continuous variable—using all available predictors simultaneously. This method shows you how well the variables collectively predict the outcome while controlling for the effects of other variables. It provides an overall model fit statistic (R-squared) and allows you to assess each predictor's unique contribution. Multiple correlation analysis (A) only examines the strength of relationships but doesn't create a predictive model. While correlation is useful for understanding associations, it doesn't help you make actual predictions or determine how much variance in purchase amounts your variables explain. Logistic regression (B) is designed for categorical outcomes, not continuous ones like purchase amount. You'd only use this if you converted purchase amount into categories (high/low), but doing so would waste valuable information and reduce analytical power. Running separate simple linear regressions (C) misses the whole point of multivariate analysis. Individual regressions can't show you the combined predictive power of your variables or control for confounding effects. A variable might appear important individually but become nonsignificant when other predictors are included. Study tip: Remember that multiple linear regression is your go-to method when predicting continuous outcomes with multiple predictors. If the outcome is categorical, think logistic regression. If you only want to measure relationships without prediction, consider correlation analysis.

Question 7

A manufacturing process has a specification that a certain component's length must be 100 mm ± 2 mm. An engineer takes a sample of 50 components and finds the sample mean is 100.5 mm and the sample standard deviation is 0.5 mm. The engineer wants to assess whether the process is capable of consistently producing parts within the specification limits, considering both the process center and its variation. Which type of analysis is most appropriate?

  1. A process capability analysis (e.g., calculating the Cpk index) to compare the process spread to the specification width. (correct answer)
  2. A control chart analysis (e.g., X-bar and R chart) to monitor the process stability over time.
  3. A one-sample t-test to confirm if the process mean is significantly different from the target of 100 mm.
  4. A hypothesis test for the population standard deviation to ensure it is less than a certain threshold.
Explanation: When you encounter a question asking whether a manufacturing process can consistently meet specification limits, you're dealing with process capability analysis. This differs from simply testing if the current sample meets specs—you need to evaluate the process's long-term ability to stay within bounds given its natural variation. Answer A is correct because process capability analysis, particularly the Cpk index, directly addresses this question. Cpk measures how well a process can perform relative to specification limits, accounting for both the process center (mean) and spread (standard deviation). With specifications of 100 ± 2 mm, a sample mean of 100.5 mm, and standard deviation of 0.5 mm, calculating Cpk would show whether this process variation can consistently stay within the 98-102 mm range. Answer B is wrong because control charts monitor process stability over time to detect when a process goes "out of control." While useful for ongoing monitoring, they don't directly assess capability against specification limits. Answer C is incorrect because a one-sample t-test only tells you if the current mean differs significantly from target—it ignores process variation entirely. You could have a mean exactly at 100 mm but still produce many defective parts if variation is too high. Answer D is flawed because testing the standard deviation alone doesn't consider where the process is centered relative to specifications. A low standard deviation is useless if the process mean is off-target. Remember: capability analysis questions ask "Can this process consistently meet specs?" while control chart questions ask "Is this process stable?" and hypothesis tests ask "Is this sample significantly different?"

Question 8

A financial services company wants to determine if there are differences in average account balances among customers from four different geographic regions. They have account balance data for random samples of customers from each region: Northeast (n=35), Southeast (n=42), Midwest (n=38), and West (n=41). Initial analysis suggests the account balance distributions may have different variances across regions.

Given the potential for unequal variances across regions, which statistical approach should be used to test for differences in mean account balances?

  1. Standard one-way ANOVA assuming equal variances followed by Tukey's HSD post-hoc test for pairwise comparisons if significant
  2. Kruskal-Wallis test as a non-parametric alternative that doesn't require assumptions about variance equality or normality
  3. Welch's ANOVA (unequal variances ANOVA) followed by appropriate post-hoc tests that don't assume equal variances (correct answer)
  4. Multiple two-sample t-tests with Welch's correction for unequal variances comparing each pair of regions independently
Explanation: When you encounter a question about comparing means across multiple groups with potential variance differences, you're dealing with ANOVA assumptions and their violations. The key insight is recognizing that standard ANOVA requires homogeneity of variance (equal variances), and when this assumption is violated, you need specialized approaches. Welch's ANOVA (option C) is specifically designed for situations where group variances are unequal. It adjusts the degrees of freedom and test statistic to account for heteroscedasticity, making it the most appropriate choice when you suspect variance differences across groups. The follow-up post-hoc tests would similarly account for unequal variances. Option A is incorrect because standard one-way ANOVA assumes equal variances across groups. Using it when variances differ can lead to inflated Type I error rates and unreliable conclusions. Tukey's HSD also assumes equal variances, compounding the problem. Option B, the Kruskal-Wallis test, is overly conservative here. While it doesn't assume equal variances or normality, it's a non-parametric test that sacrifices power when your data might still be suitable for parametric analysis. The passage doesn't indicate normality violations, only variance differences. Option D creates a multiple comparisons problem. Conducting separate t-tests increases the family-wise error rate dramatically. Even with Welch's correction for each test, you're not controlling for the overall Type I error across all comparisons. Study tip: When you see "unequal variances" with multiple groups, think Welch's ANOVA first. Save non-parametric tests for when you have both variance and normality violations.

Question 9

A marketing team at an e-commerce company wants to determine if a new, simplified checkout page design (Design B) results in a statistically significant higher conversion rate compared to the current design (Design A). They randomly assign 1,000 visitors to Design A and 1,000 visitors to Design B, recording how many from each group complete a purchase. Which statistical method is most appropriate for this business question?

  1. A two-sample t-test to compare the mean number of conversions between the two designs.
  2. A paired t-test to analyze the difference in performance since the designs are being compared.
  3. A two-proportion z-test to determine if the proportion of conversions for Design B is greater than for Design A. (correct answer)
  4. A chi-squared test for independence to see if a relationship exists between page design and the number of visitors.
Explanation: The business question is about comparing two conversion rates, which are proportions. The data consists of counts of successes (conversions) and failures for two independent groups. Therefore, a two-proportion z-test is the most direct and appropriate method to determine if one proportion is significantly higher than the other.

Question 10

A national retail chain is testing three new store layouts (Layout X, Layout Y, Layout Z) to see if they impact customer satisfaction. The company surveys a random sample of 100 shoppers from each layout type, asking them to rate their experience on a scale of 1 to 10. The primary goal is to determine if there is any statistically significant difference in the mean satisfaction scores among the three layouts. What is the most suitable statistical test?

  1. Conducting three separate independent two-sample t-tests (X vs. Y, Y vs. Z, X vs. Z) to compare each pair of layouts.
  2. A single Analysis of Variance (ANOVA) test to compare the means of the three groups simultaneously. (correct answer)
  3. A multiple regression model with store layout as the predictor and satisfaction score as the response variable.
  4. A chi-squared goodness-of-fit test to see if the distribution of satisfaction scores is the same across layouts.
Explanation: The goal is to compare the means of a numerical variable (satisfaction score) across three independent groups (the layouts). A one-way ANOVA is the correct procedure for this, as it controls the overall Type I error rate. Conducting multiple t-tests would inflate this error rate, a problem known as multiple comparisons.

Question 11

An HR department implemented a mandatory professional development workshop for its 45-person sales team. To measure its effectiveness, they recorded the total sales value for each salesperson in the month before the workshop and the month after. The department wants to know if the workshop led to a statistically significant increase in the average sales value. Which method should be used?

  1. An independent two-sample t-test, treating the 'before' and 'after' results as two separate groups of sales data.
  2. A paired t-test, analyzing the mean of the differences between each salesperson's 'after' and 'before' sales values. (correct answer)
  3. A one-way ANOVA to determine if there is a difference between the two time periods.
  4. A Pearson correlation analysis to measure the strength of the relationship between 'before' and 'after' sales performance.
Explanation: This scenario involves comparing two measurements taken from the same subjects (each salesperson). The data points are paired. A paired t-test is the correct method because it analyzes the differences within each pair, which controls for individual variations among salespeople and increases the statistical power of the test.

Question 12

A financial analyst wants to build a model to predict the quarterly revenue of a tech company. The analyst has collected data for the past 20 quarters on the company's R&D spending, marketing budget, and number of new software releases. The goal is to create an equation that estimates revenue based on these three variables. Which statistical technique is most appropriate for this predictive task?

  1. A time series analysis using ARIMA to forecast future revenue based on its past values.
  2. A multiple linear regression to model the relationship between the three predictor variables and quarterly revenue. (correct answer)
  3. An Analysis of Variance (ANOVA) to see which of the three variables has the largest impact on revenue.
  4. A correlation matrix to determine the individual strength of association between each variable and revenue.
Explanation: The objective is to create a predictive model that uses multiple numerical independent variables (R&D spending, marketing budget, releases) to estimate a single numerical dependent variable (revenue). This is the primary application of multiple linear regression.

Question 13

A supply chain manager is evaluating a new supplier of microchips. The company's quality standard requires that the proportion of defective chips be no more than 1.5%. The manager tests a random sample of 500 chips from the new supplier and finds 11 defects. To decide whether the supplier meets the standard, which statistical test should be performed?

  1. A one-sample t-test to compare the sample mean number of defects to the 1.5% standard.
  2. A two-proportion z-test to compare the defective rate of the new supplier to the old one.
  3. A one-proportion z-test to determine if the sample proportion of defects (11/500) is significantly greater than the 1.5% threshold. (correct answer)
  4. A chi-squared goodness-of-fit test to see if the observed number of defects fits the expected number based on the standard.
Explanation: This problem involves testing a claim about a single population proportion (the defective rate of the new supplier) against a known value (1.5%). The data is categorical (defective/not defective). Therefore, a one-proportion z-test is the appropriate method.

Question 14

A project manager observes that project completion times for her four teams seem to vary widely. She collects the completion times for the last 10 projects for each team. A preliminary analysis reveals that the data for two of the teams is highly right-skewed and contains several large outliers. To determine if there is a statistically significant difference in the typical completion time among the four teams, which test is most robust and appropriate?

  1. A standard one-way ANOVA, because it is the conventional method for comparing means of four groups.
  2. The Kruskal-Wallis test, as it is a non-parametric alternative to ANOVA that compares medians and is not sensitive to outliers. (correct answer)
  3. The Mann-Whitney U test, applied to each pair of teams to identify specific differences in project completion times.
  4. An F-test for equality of variances to first confirm if the variability in completion times is different across the teams.
Explanation: The presence of high skewness and outliers violates the normality assumption of a standard ANOVA test. The Kruskal-Wallis test is the appropriate non-parametric alternative for comparing the central tendency (medians) of three or more independent groups when the assumptions for ANOVA are not met.

Question 15

A subscription-based service wants to build a model to predict whether a customer will cancel their subscription (churn) in the next month. They have data on each customer's monthly usage hours, tenure with the service (in months), and whether they have filed a support ticket in the last 90 days. The outcome variable is binary: 'Churn' or 'No Churn'. Which method is most suitable for creating this predictive model?

  1. Multiple linear regression to calculate a 'churn score' based on the predictor variables.
  2. A two-sample t-test to compare the average tenure of customers who churn versus those who do not.
  3. Logistic regression to estimate the probability of churn based on the customer's attributes. (correct answer)
  4. K-means clustering to group customers into 'high-risk' and 'low-risk' segments based on their behavior.
Explanation: The goal is to predict a binary categorical outcome (Churn/No Churn) based on several predictor variables. Logistic regression is the standard statistical method for this type of problem, as it models the probability of the outcome occurring.

Question 16

A food scientist is developing a new gluten-free bread and wants to study the effects of baking temperature (350°F, 400°F) and the type of flour used (Almond, Buckwheat) on the bread's rated moisture level. The scientist wants to determine not only the individual effect of temperature and flour, but also if a particular combination of temperature and flour (an interaction effect) yields a uniquely high or low moisture level. Which analytical approach is most appropriate?

  1. Two separate one-way ANOVA tests: one to compare temperatures and another to compare flours.
  2. A multiple linear regression model with temperature and flour type as predictors.
  3. A two-way ANOVA to analyze the main effects of temperature and flour, as well as their interaction effect. (correct answer)
  4. A series of independent t-tests comparing all four combinations (e.g., 350°F/Almond vs 400°F/Almond).
Explanation: This is a classic factorial experimental design with two categorical independent variables (factors) and one continuous dependent variable. A two-way ANOVA is the correct method because it can simultaneously test for the main effects of each factor and, crucially, for the interaction effect between them, which is a specific goal of the study.

Question 17

A financial services company's risk model assumes that the daily returns on a particular portfolio are normally distributed. To validate this critical assumption, a risk analyst collects a sample of 200 daily returns. Which of the following is the most appropriate formal statistical procedure to test if the sample data plausibly came from a normal distribution?

  1. A one-sample t-test to check if the mean return of the sample is equal to zero.
  2. The Central Limit Theorem to argue that the sample mean will be normally distributed.
  3. A chi-squared test for variance to see if the sample variance matches a theoretical value.
  4. A goodness-of-fit test, such as the Shapiro-Wilk or Kolmogorov-Smirnov test. (correct answer)
Explanation: The question is about formally testing the distributional shape of the data, not its parameters like the mean or variance. Goodness-of-fit tests like Shapiro-Wilk or Kolmogorov-Smirnov are specifically designed to test the null hypothesis that a sample of data comes from a specified distribution, such as the normal distribution.

Question 18

A UX designer wants to determine if there is a statistically significant relationship between the time a user spends on a product page (a continuous variable measured in seconds) and whether they ultimately make a purchase (a binary variable: Yes/No). Which method is most appropriate for investigating this specific question?

  1. An independent two-sample t-test, to compare the mean time spent for purchasers versus non-purchasers. (correct answer)
  2. A chi-squared test of independence, after grouping the time spent into categories.
  3. Pearson correlation, which requires both variables to be continuous and normally distributed.
  4. Simple linear regression, with time spent as the predictor for the binary purchase outcome.
Explanation: When you encounter a question about analyzing the relationship between a continuous variable and a binary outcome, you need to identify which statistical method properly handles this specific data structure. Option A is correct because an independent two-sample t-test is designed exactly for this situation. You would compare the mean time spent on product pages between two groups: users who purchased (Yes) and users who didn't purchase (No). This test determines whether the difference in average time between these groups is statistically significant, directly answering whether purchase behavior is related to time spent. Option B is problematic because converting the continuous time variable into categories throws away valuable information. While a chi-squared test could work after categorization, this approach reduces statistical power and isn't the most appropriate method when you have precise continuous measurements. Option C fails because Pearson correlation requires both variables to be continuous. Your purchase variable is binary (Yes/No), not continuous, making this method inappropriate for the data structure you have. Option D represents a common confusion. While you could technically run linear regression with a binary outcome, this violates key assumptions of linear regression (the outcome should be continuous and normally distributed). The predicted values could fall outside the 0-1 range, making interpretation problematic. Study tip: When you see continuous vs. binary comparisons, think "two-sample t-test." When you see two continuous variables, think "correlation or regression." Matching the statistical method to your variable types is crucial for valid analysis.

Question 19

A fast-food chain is considering a new promotional item. To gauge interest, they conduct a survey in two different cities, asking 200 people in each city whether they would be 'likely to try' the new item. In City A, 88 people said yes. In City B, 104 people said yes. The marketing director wants to know if the difference in the proportion of interested customers between the two cities is statistically significant. Which method should be used?

  1. A chi-squared test of independence to see if city and interest are related.
  2. An independent two-sample t-test to compare the mean interest level in the two cities.
  3. A paired t-test because the survey question was the same in both cities.
  4. A two-proportion z-test to compare the sample proportions from the two independent city samples. (correct answer)
Explanation: The goal is to compare a proportion (proportion of interested customers) between two independent groups (City A and City B). The two-proportion z-test is the standard statistical method for this purpose. A chi-squared test would yield a similar conclusion but the z-test is more direct for comparing two proportions and can easily accommodate one-tailed tests.

Question 20

A manufacturing company produces widgets with a target weight of 100 grams. Quality control has been monitoring production for potential changes in the manufacturing process. Historical data shows the process has been stable with a known standard deviation of 5 grams. Today, a sample of 25 widgets was collected.

If the quality control manager wants to test whether the current production process mean has shifted from the target weight, which combination of test and conditions is most appropriate?

  1. One-sample z-test, assuming the population standard deviation is known and the sampling distribution is approximately normal (correct answer)
  2. One-sample t-test, because the sample size is less than 30 and population standard deviation is unknown
  3. Two-sample t-test comparing current sample mean against historical mean with unequal variances assumed
  4. Paired t-test comparing each widget weight against the target weight of 100 grams for dependency
Explanation: A one-sample z-test is appropriate because: (1) the population standard deviation is known (5 grams), (2) we're comparing a sample mean to a known target value (100 grams), and (3) the sample size (25) is sufficient for normal approximation. Option B is wrong because the population standard deviation IS known. Option C is incorrect because we're not comparing two independent samples. Option D is wrong because we don't have paired measurements - we're comparing sample mean to a fixed target value, not paired differences.