AP Statistics - AP Statistics
Card 0 of 1368
A prominent football coach is being reviewed for his performance in the past season. To evaluate how well the coach has done, the team manager runs a statistical test comparing the coach to a sample of coaches in the league. If the test suggests that the coach outperformed other coaches when in fact he did not, and the manager then rejects the null hypothesis (that the coach did not outperform the other coaches), what kind of error is he committing?
A prominent football coach is being reviewed for his performance in the past season. To evaluate how well the coach has done, the team manager runs a statistical test comparing the coach to a sample of coaches in the league. If the test suggests that the coach outperformed other coaches when in fact he did not, and the manager then rejects the null hypothesis (that the coach did not outperform the other coaches), what kind of error is he committing?
A type I error occurs when one rejects a null hypothesis that is in fact true. The null hypothesis is that the coach does not outperform other coaches, and the test reccomends that we reject it even though it is true. Thus, a type I error has been committed.
A type I error occurs when one rejects a null hypothesis that is in fact true. The null hypothesis is that the coach does not outperform other coaches, and the test reccomends that we reject it even though it is true. Thus, a type I error has been committed.
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If a hypothesis test uses a 
confidence level, then what is its probability of Type I Error?
If a hypothesis test uses a
By definition, the probability of Type I Error is,
where,
represents Probability of Type I Error and 
represents the confidence level.
Thus resulting in:
By definition, the probability of Type I Error is,
where,
Thus resulting in:
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For significance tests, which of the following is an incorrect way to increase power (the probability of correctly rejecting the null hypothesis)?
For significance tests, which of the following is an incorrect way to increase power (the probability of correctly rejecting the null hypothesis)?
Recall that power is 
. The probability of Type I and Type II errors will change inversely of each other as the probability of making a Type I error changes. If 
increases, then 
decreases, and as a result power will increase. So if 
decreases, 
would increase, and power would decrease; therefore decreasing 
will not increase power.
Recall that power is
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In a recent athletic study, your lab partner told you that they rejected the null hypothesis that the fabric of running shoes has no effect on the wearer's running times.
If the null hypothesis was actually valid, what type of error was made?
In a recent athletic study, your lab partner told you that they rejected the null hypothesis that the fabric of running shoes has no effect on the wearer's running times.
If the null hypothesis was actually valid, what type of error was made?
A type I error occurs when the null hypothesis is valid but rejected.
A type II error occurs when the null hypothesis is false, but fails to be rejected.
Because the null hypothesis was true, but rejected, they made a Type I error.
A type I error occurs when the null hypothesis is valid but rejected.
A type II error occurs when the null hypothesis is false, but fails to be rejected.
Because the null hypothesis was true, but rejected, they made a Type I error.
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In a recent academic study, your lab partner told you that they rejected the null hypothesis that the ionization of water has no effect on the rate of grass growth.
If the null hypothesis was actually valid, what type of error was made?
In a recent academic study, your lab partner told you that they rejected the null hypothesis that the ionization of water has no effect on the rate of grass growth.
If the null hypothesis was actually valid, what type of error was made?
A type I error occurs when the null hypothesis is valid but rejected.
A type II error occurs when the null hypothesis is false, but fails to be rejected.
Because the null hypothesis was true, but rejected, they made a Type I error.
A type I error occurs when the null hypothesis is valid but rejected.
A type II error occurs when the null hypothesis is false, but fails to be rejected.
Because the null hypothesis was true, but rejected, they made a Type I error.
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A company claims that they have 12 ounces of potato chips in each of their bags of chips. A customer complaint is filed that they do not truly contain 12 ounces but actually contain less. A sampling test is conducted to see if the comapny measure is true or not. What would be an example of a Type I error?
A company claims that they have 12 ounces of potato chips in each of their bags of chips. A customer complaint is filed that they do not truly contain 12 ounces but actually contain less. A sampling test is conducted to see if the comapny measure is true or not. What would be an example of a Type I error?
The type I error is rejecting the null hypothesis when it is actually true. The null here is 12 ounces per bag so a type I error would be rejecting the company claim even though there are 12 ounces per bag.
The type I error is rejecting the null hypothesis when it is actually true. The null here is 12 ounces per bag so a type I error would be rejecting the company claim even though there are 12 ounces per bag.
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Obtain a normal distribution table or calculator for this problem.
Approximate the 
-percentile on the standard normal distribution.
Obtain a normal distribution table or calculator for this problem.
Approximate the
The 
-percentile is the value such that 
percent of values are less than it.
Using a normal table or calculator (such as R, using the command qnorm(0.9)), we get that the approximate 
-percentile is about 
.
The
Using a normal table or calculator (such as R, using the command qnorm(0.9)), we get that the approximate
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Find the first and third quartile for the set of data
Find the first and third quartile for the set of data
In order to find the first and third quartiles, we haave to find the 25th and 75th percentiles, respectively.
To find the 
percentile, we find the product of 
and the number of items 
in the set.
We then round that number 
up if it is not a whole number, and the 
term in the set is the 
percentile.
For this problem, to find the 
and 
percentile, we first find that there are 14 items in the set. We find their respective products to be
and
As such, the 
and 
percentiles are the fourth and eleventh terms in the set, or
In order to find the first and third quartiles, we haave to find the 25th and 75th percentiles, respectively.
To find the
We then round that number
For this problem, to find the
As such, the
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Use the following five number summary to determine if there are any outliers in the data set:
Minimum: 
Q1: 
Median: 
Q3: 
Maximum: 
Use the following five number summary to determine if there are any outliers in the data set:
Minimum:
Q1:
Median:
Q3:
Maximum:
An observation is an outlier if it falls more than 
above the upper quartile or more than 
below the lower quartile.
. The minimum value is 
so there are no outliers in the low end of the distribution.
. The maximum value is 
so there are no outliers in the high end of the distribution.
An observation is an outlier if it falls more than
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For a data set, the first quartile is 
, the third quartile is 
and the median is 
.
Based on this information, a new observation can be considered an outlier if it is greater than what?
For a data set, the first quartile is
Based on this information, a new observation can be considered an outlier if it is greater than what?
Use the 
criteria:
This states that anything less than 
or greater than 
will be an outlier.
Thus, we want to find
where 
.
Therefore, any new observation greater than 115 can be considered an outlier.
Use the
This states that anything less than
Thus, we want to find
Therefore, any new observation greater than 115 can be considered an outlier.
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Which values in the above data set are outliers?
Which values in the above data set are outliers?
Step 1: Recall the definition of an outlier as any value in a data set that is greater than 
or less than 
.
Step 2: Calculate the IQR, which is the third quartile minus the first quartile, or 
. To find 
and 
, first write the data in ascending order.
. Then, find the median, which is 
. Next, Find the median of data below 
, which is 
. Do the same for the data above 
to get 
. By finding the medians of the lower and upper halves of the data, you are able to find the value, 
that is greater than 25% of the data and 
, the value greater than 75% of the data.
Step 3: 
. No values less than 64.
. In the data set, 105 > 104, so it is an outlier.
Step 1: Recall the definition of an outlier as any value in a data set that is greater than
Step 2: Calculate the IQR, which is the third quartile minus the first quartile, or
Step 3:
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You are given the following information regarding a particular data set:
Q1: 
Q3: 
Assume that the numbers 
and 
are in the data set. How many of these numbers are outliers?
You are given the following information regarding a particular data set:
Q1:
Q3:
Assume that the numbers
In order to find the outliers, we can use the 
and 
formulas.
Only two numbers are outside of the calculated range and therefore are outliers: 
and 
.
In order to find the outliers, we can use the
Only two numbers are outside of the calculated range and therefore are outliers:
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Use the following five number summary to answer the question below:
Min: 
Q1: 
Med: 
Q3: 
Max: 
Which of the following is true regarding outliers?
Use the following five number summary to answer the question below:
Min:
Q1:
Med:
Q3:
Max:
Which of the following is true regarding outliers?
Using the 
and 
formulas, we can determine that both the minimum and maximum values of the data set are outliers.
This allows us to determine that there is at least one outlier in the upper side of the data set and at least one outlier in the lower side of the data set. Without any more information, we are not able to determine the exact number of outliers in the entire data set.
Using the
This allows us to determine that there is at least one outlier in the upper side of the data set and at least one outlier in the lower side of the data set. Without any more information, we are not able to determine the exact number of outliers in the entire data set.
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A certain distribution has a 1st quartile of 8 and a 3rd quartile of 16. Which of the following data points would be considered an outlier?
A certain distribution has a 1st quartile of 8 and a 3rd quartile of 16. Which of the following data points would be considered an outlier?
An outlier is any data point that falls 
above the 3rd quartile and below the first quartile. The inter-quartile range is 
and 
. The lower bound would be 
and the upper bound would be 
. The only possible answer outside of this range is 
.
An outlier is any data point that falls
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Obtain a normal distribution table or calculator for this problem.
Approximate the -percentile on the standard normal distribution.
Obtain a normal distribution table or calculator for this problem.
Approximate the
The -percentile is the value such that percent of values are less than it.
Using a normal table or calculator (such as R, using the command qnorm(0.9)), we get that the approximate -percentile is about .
The
Using a normal table or calculator (such as R, using the command qnorm(0.9)), we get that the approximate
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Find the first and third quartile for the set of data
Find the first and third quartile for the set of data
In order to find the first and third quartiles, we haave to find the 25th and 75th percentiles, respectively.
To find the percentile, we find the product of and the number of items in the set.
We then round that number up if it is not a whole number, and the term in the set is the percentile.
For this problem, to find the and percentile, we first find that there are 14 items in the set. We find their respective products to be
and
As such, the and percentiles are the fourth and eleventh terms in the set, or
In order to find the first and third quartiles, we haave to find the 25th and 75th percentiles, respectively.
To find the
We then round that number
For this problem, to find the
As such, the
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A study is trying to determine if a particular medication (Y) is effective in weight loss. Patients participating in the study were randomly assigned to groups A, B, C, D, or E. Group A will receive one dose of Y, Group B will receive two doses of Y, Group C will receive three doses of Y, Group D will receive four doses of Y, and Group E will serve as the control group.
Which group will be receiving the placebo (a sugar pill)?
A study is trying to determine if a particular medication (Y) is effective in weight loss. Patients participating in the study were randomly assigned to groups A, B, C, D, or E. Group A will receive one dose of Y, Group B will receive two doses of Y, Group C will receive three doses of Y, Group D will receive four doses of Y, and Group E will serve as the control group.
Which group will be receiving the placebo (a sugar pill)?
The control group in an experiment typically receives placebo treatments (in this case - Group E). Since all of the other groups are receiving at least one dose of the medication, they are considered to be experimental groups.
The control group in an experiment typically receives placebo treatments (in this case - Group E). Since all of the other groups are receiving at least one dose of the medication, they are considered to be experimental groups.
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To test if vitamin C actually makes people feel better, a vitamin company decides to run a 5-day study where they give one group of 100 sick participants vitamin C pills and another group of 100 sick people placebo pills, and monitored another group of 100 sick people who took no pills.
At the end of the 5-day experiment, 90 participants in the vitamin C group reported feeling better. 30 participants in the no-pill group felt better after the 5-day period. Interestingly, 50 participants in the placebo group felt better after the 5-day period.
What could explain these numbers?
To test if vitamin C actually makes people feel better, a vitamin company decides to run a 5-day study where they give one group of 100 sick participants vitamin C pills and another group of 100 sick people placebo pills, and monitored another group of 100 sick people who took no pills.
At the end of the 5-day experiment, 90 participants in the vitamin C group reported feeling better. 30 participants in the no-pill group felt better after the 5-day period. Interestingly, 50 participants in the placebo group felt better after the 5-day period.
What could explain these numbers?
The placebo effect is when effects are seen in a group of people who did not actually receive a treatment.
In the vitamin C group, 90 participants felt better.
Naturally (no-pill), 30 participants felt better.
With the placebo, 50 participants felt better. Since more people felt better with the placebo than with no treatment at all, it appears that some percentage of people believed that they would feel better with a pill and actually began to feel better due to the placebo effect.
The placebo effect is when effects are seen in a group of people who did not actually receive a treatment.
In the vitamin C group, 90 participants felt better.
Naturally (no-pill), 30 participants felt better.
With the placebo, 50 participants felt better. Since more people felt better with the placebo than with no treatment at all, it appears that some percentage of people believed that they would feel better with a pill and actually began to feel better due to the placebo effect.
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What is 
, or the expected value of 
for any distribution?
What is
is 
, or the mean, of the population. This makes sense since 
literally means the expected value of 
. The mean is the expected value of 
.
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No explanation available
No explanation available
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