Practice Test 41 - AP Statistics

20 questions. Answer them in any order, then submit to see your score and every explanation.

A restaurant chain wants to know whether changing its menu layout affects the proportion of customers who order a dessert. At 40 randomly selected locations using the old menu, 92 of 400 customers ordered dessert ( $\hat{p}_O=0.23$ ). At 35 independently selected locations using the new menu, 126 of 420 customers ordered dessert ( $\hat{p}_N=0.30$ ). The research claim is that the new menu changes (not necessarily increases) the dessert-ordering rate. Which hypotheses are appropriate?
A company randomly sampled 600 customers who made a purchase last month to estimate the proportion $p$ who were satisfied with their experience. In the sample, 510 customers reported being satisfied. A 99% confidence interval for $p$ was computed as $(0.82, 0.88)$ . Which interpretation is correct?
A county health department wants to estimate the proportion of adults who received a flu shot this season. Two independent simple random samples are taken from the same county adult population: Sample A of 300 adults finds 41% received a flu shot; Sample B of 300 different adults finds 45%. Why might the sample results differ?
A streaming service wants to see whether subscription plan is associated with hours streamed per week. For each of 200 randomly selected users, the company records the user's plan (coded 0 = basic, 1 = standard, 2 = premium) and the number of hours the user streamed content in the last 7 days. The observational units are the users. Which classification is correct?
A company wants to estimate the mean satisfaction score (1–10) among all employees. The company has 12 departments and randomly selects 3 departments, then surveys every employee in those 3 departments. Which statement best describes the sample representativeness?
A quality-control manager records the fill amounts (in ounces) for a random sample of 58 bottles from a beverage-filling machine to assess how often bottles are underfilled. Why is a normal model reasonable for the fill amounts?
A biology teacher wants to estimate the mean height (in centimeters) of a certain species of plant in a large greenhouse. The teacher randomly selects 18 plants and measures their heights. A 95% confidence interval for the population mean plant height is reported as $(42.1,\ 47.9)$ cm. Which interpretation is correct?
A city analyst records average daily temperature ( $x$ , in $^\circ$ F) and electricity use ( $y$ , in kWh) for 15 spring days. A least-squares regression line is fit to predict electricity use from temperature: $\hat{y}=980-7.5x$ . The purpose of this linear model is to describe the linear relationship and predict typical electricity use for temperatures within the observed range. Which interpretation of the model is correct?
In a factory, let $P$ be the time (in seconds) to assemble Part 1 and $Q$ be the time (in seconds) to assemble Part 2 for a randomly selected unit. Over many units, $\mu_P=35$ with $\sigma_P=6$ , and $\mu_Q=45$ with $\sigma_Q=9$ . Assume $P$ and $Q$ are independent. Define total assembly time $T=P+Q$ . Which statement about $T$ is correct?
A city compares mean monthly electricity usage (kWh) between homes with solar panels (group P) and similar homes without solar panels (group N). Independent random samples were taken from each group. A two-sample $t$ test was performed for $H_0: \mu_P-\mu_N=0$ versus $H_a: \mu_P-\mu_N<0$ . The p-value was 0.12. Using $\alpha=0.05$ , what conclusion is appropriate?
A researcher tests 10 seeds by planting each one and recording whether it germinates (success) within 7 days. For this type of seed, the probability of germination is 0.65 under the same conditions, and the researcher treats each seed's outcome as independent. Let $X$ be the number of seeds that germinate. Which values correctly model this situation?
A teacher compared two homework policies (Optional vs Required) and noted whether students turned in the assignment (Turned in/Did not turn in). The purpose is to compare conditional proportions of turning in homework by policy. Based on the two-way table, which comparison is supported? Two-way table of Policy by Turn-in Status (proportions of all students): - Optional & Turned in: 0.21, Optional & Did not: 0.29 - Required & Turned in: 0.36, Required & Did not: 0.14
An environmental scientist compares mean nitrate concentration (mg/L) in water from wells near farms vs wells far from farms. Using two independent random samples, a 95% confidence interval for $(\mu_{near}-\mu_{far})$ is $(1.1, 3.6)$ . Which interpretation is correct?
A farmer wants to determine whether fertilizer type is related to corn yield. For each of 30 fields, the farmer records the fertilizer type used (A, B, or C) and the yield in bushels per acre at harvest. The observational units are the fields. Which classification is correct?
A streaming service wants to estimate the mean number of hours subscribers watch per week. Two independent simple random samples of 60 subscribers are selected from the same subscriber database during the same week. Sample X has a mean of 11.2 hours; Sample Y has a mean of 9.7 hours. Why might the sample results differ?
Two tutoring methods are compared using mean improvement on a math test (points). Method 1 had a sample mean improvement of 12.3 points and Method 2 had 11.7 points. A 95% confidence interval for the difference in population means, defined as $\mu_1-\mu_2$ , is $(-0.4, 1.6)$ . A teacher claims, "Method 1 produces a higher mean improvement than Method 2." Is the claim supported by the confidence interval?
A delivery service claims that 90% of its packages arrive on time. A customer tracks 15 packages and finds that 11 arrive on time. The customer expected about 14 on-time deliveries but observed 11. Is the result unexpected, given the variability with only 15 packages?
A soda company claims that among all cans produced, the distribution of fill-level categories is 2% underfilled, 96% correctly filled, and 2% overfilled. A random sample of 500 cans is inspected, and the observed counts are shown below. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the company's claim?
An online retailer claims that orders are shipped using three carriers in the following proportions: Carrier A 50%, Carrier B 35%, Carrier C 15%. A random sample of $n=180$ recent orders is selected, and the observed counts are shown in a table. Which hypotheses are appropriate for a chi-square goodness-of-fit test of the retailer's claim?
A marketing manager investigates whether the number of online ads shown per week ( $x$ ) predicts weekly sales revenue in dollars ( $y$ ). The manager suspects that showing more ads increases sales in the population. Which hypotheses are appropriate for testing the manager's claim about the slope of the population regression line?

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