Module 3 (Hypothesis Testing) Flashcards
Classify each of the following as either one-sided or two-sided hypothesis tests:
A - Test whether incoming students at a business school receive better grades in their classes if they’ve taken an on-line program covering basic material
B - Test whether there is a difference between men’s and women’s usage of a mobile fitness app
C - Test whether the number of listeners of a streaming music service has changed after they changed the user interface
D - Test whether users of a commercial website are less likely to make a purchase if they are required to set up a user account on the site
A + D: One-sided
B + C: Two-sided
A movie theater manager wants to determine whether popcorn sales have increased since the theater switched from using “butter-flavored topping” to real butter. Historically the average popcorn revenue per weekend day was approximately $3,500. After the theater started using real butter, the manager randomly sampled 12 weekend days and calculated the sample’s summary statistics. The average revenue per weekend day in the sample was approximately $4,200 with a standard deviation of $140.
Select the function that would correctly calculate the 90% range of likely sample means.
A - 3,500±CONFIDENCE.T(0.10,140,12)
B - 4,200±CONFIDENCE.T(0.10,140,12)
C - 3,500±CONFIDENCE.NORM(0.10,140,12)
D - 4,200±CONFIDENCE.NORM(0.10,140,12)
A - 3,500±CONFIDENCE.T(0.10,140,12)
The range of likely sample means is centered at the historical population mean, in this case $3,500. Because the sample contains fewer than 30 data points, we use CONFIDENCE.T. Excel’s CONFIDENCE.T function syntax is CONFIDENCE.T(alpha, standard_dev, size). Because we wish to construct a 90% range of likely sample means, alpha equals 0.10.
The owner of a local health food store recently started a new ad campaign to attract more business and wants to test whether average daily sales have increased. Historically average daily sales were approximately $2,700. After the ad campaign, the owner took a random sample of forty-five days and found that daily average sales had increased to $2,984.
What is store owner’s null hypothesis?
Recall that the owner of a local health food store recently started a new ad campaign to attract more business and wants to know if average daily sales have increased. Historically average daily sales were approximately $2,700. The upper bound of the 95% range of likely sample means for this one-sided test is approximately $2,843.44.
If the owner took a random sample of forty-five days and found that daily average sales were now $2,984, what can she conclude at the 95% confidence level?
Average daily sales have increased
Since the sample mean, $2,984, falls outside the range of likely sample means (which has an upper bound=$2,843.44), the store owner can reject the null hypothesis that at a 95% confidence level. Since she can reject the null hypothesis, she can essentially accept the alternative hypothesis and conclude the average daily sales have increased.
A college student is interested in testing whether business majors or liberal arts majors are better at trivia. The student gives a trivia quiz to a random sample of 30 business majors and finds the sample’s average score is 86. He gives the same quiz to 30 randomly selected liberal arts majors and finds the sample’s average score is 89.
What is the alternative hypothesis of this test?
A college student is interested in testing whether business majors or liberal arts majors are better at trivia. The student gives a trivia quiz to a random sample of 30 business school majors and finds the sample’s average test score is 86. He gives the same quiz to 30 randomly selected liberal arts majors and finds the sample’s average quiz score is 89. The student finds that the p-value for the hypothesis test equals approximately 0.0524.
What can be concluded at ∂=5%?
A - The student should reject the null hypothesis and conclude that there is insufficient evidence of difference between business and liberal arts majors’ knowledge of trivia.
B - The student should reject the null hypothesis and conclude that there is a significant difference between business and liberal arts majors’ knowledge of trivia.
C - The student should fail to reject the null hypothesis and conclude that there is insufficient evidence of difference between business and liberal arts majors’ knowledge of trivia.
D - The student should fail to reject the null hypothesis and conclude that there is a significant difference between business and liberal arts majors’ knowledge of trivia.
C - The student should fail to reject the null hypothesis and conclude that there is insufficient evidence of difference between business and liberal arts majors’ knowledge of trivia.
A type I error is often called a ___________, in which we incorrectly___________.
The probability of making a type I error is equal to __________.
A type I error is often called a false positive (we incorrectly reject the null hypothesis when it is actually true)
The probability of a type I error is equal to the significance level (which is 1–confidence level).
A streaming music site changed its format to focus on previously unreleased music from rising artists. The site manager now wants to determine whether the number of unique listeners per day has changed. Before the change in format, the site averaged 131,520 unique listeners per day. Now, beginning three months after the format change, the site manager takes a random sample of 30 days and finds that the site has an average of 124,247 unique listeners per day.
What are the null and alternative hypotheses?
A streaming music site changed its format to focus on previously unreleased music from rising artists. The site manager now wants to determine whether the number of unique listeners per day has changed. Before the change in format, the site averaged 131,520 unique listeners per day. Now, beginning three months after the format change, the site manager takes a random sample of 30 days and finds that the site now has an average of 124,247 unique listeners per day. The manager finds that the p-value for the hypothesis test is approximately 0.0743.
What can be concluded at the 95% confidence level?
A - The manager should reject the null hypothesis; there is sufficient evidence that the number of unique daily listeners has likely changed.
B - The manager should reject the null hypothesis; there is not enough evidence to conclude that the number of unique daily listeners has changed.
C - The manager should fail to reject the null hypothesis; there is sufficient evidence that the number of unique daily listeners has likely changed.
D - The manager should fail to reject the null hypothesis; there is not enough evidence to conclude that the number of unique daily listeners has changed.
D - The manager should fail to reject the null hypothesis; there is not enough evidence to conclude that the number of unique daily listeners has changed.
Since the p-value, 0.0743, is greater than the significance level, 0.05, the manager should fail to reject the null hypothesis.
A streaming music site changed its format to focus on previously unreleased music from rising artists. The site manager now wants to determine whether the number of unique listeners per day has changed. Before the change in format, the site averaged 131,520 unique listeners per day. Now, beginning three months after the format change, the site manager takes a random sample of 30 days and finds that the site has an average of 124,247 unique listeners per day. The manager finds that the p-value for the hypothesis test is approximately 0.0743.
How would you interpret the p-value?
A -The likelihood that the average number of unique daily listeners per day is no longer 131,520 is 7.43%.
B - The likelihood that the manager should reject the null hypothesis is 7.43%.
C - If the average number of unique daily listeners per day is still 131,520, the likelihood of obtaining a sample with a mean at least as extreme as 124,247 is 7.43%.
D - If the average number of unique daily listeners per day is no longer 131,520, the likelihood of obtaining a sample with a mean at least as extreme as 124,247 is 7.43%.
C - If the average number of unique daily listeners per day is still 131,520, the likelihood of obtaining a sample with a mean at least as extreme as 124,247 is 7.43%.
The null hypothesis is that the average number of unique daily listeners per day has not changed, that is, it is still 131,520. Therefore, the p-value of 0.0743 indicates that if the average number of unique daily listeners is still 131,520, the likelihood of obtaining a sample with a mean at least as extreme as 124,247 is 7.43%%.
If the two-sided p-value of a given sample is 0.0020, what is the one-sided p-value for that sample mean?
A food truck operator has traditionally sold 75 bowls of noodle soup each day. He moves to a new location and after a week sees that he has averaged 85 bowls of noodle soup sales each day. He runs a one-sided hypothesis test to determine if his daily sales at the new location have increased. The p-value of the test is 0.031.
How should he interpret the p-value?
A - There is a 3.1% chance that the true mean of soup sales at the new location is 85 bowls a day.
B - There is a 96.9% chance that the true mean of soup sales at the new location is greater than 75 bowls a day.
C - There is a 96.9% chance that the sample mean of soup sales at the new location is 85 bowls a day.
D - There is a 3.1% chance of obtaining a sample with a mean of 85 or higher assuming that the true mean sales at the new location is still equal to or less than 75 bowls a day.
E - There is a 96.9% chance that the true mean of soup sales at the new location is within 3.1 bowls of 85 bowls a day.
D - There is a 3.1% chance of obtaining a sample with a mean of 85 or higher assuming that the true mean sales at the new location is still equal to or less than 75 bowls a day.
The p-value provides us with the likelihood of the sample value equal to or more extreme than the observed sample value if the null hypothesis is true. In this case the p-value of 0.031 tells us that there would be a 3.1% chance of the sample value of 85 or above being observed if the null hypothesis were true.
An automotive manufacturer has developed a new type of tire that the research team believes to increase fuel efficiency. The manufacturer wants to test if there is an increase in the mean gas mileage of mid-sized sedans that use the new type of tire, compared to 32 miles per gallon, the historic mean gas mileage of mid-sized sedans not using the new tires.
The automotive manufacturer should perform a ___1/2 sided?__________ hypothesis test to ____analyze a change in a single/compare two populations_________.
one-sided, analyze a change in a single population
Before beginning a hypothesis test, an analyst specified a significance level of 0.10.
Which of the following is true?
A - There is a 90% chance that the alternative hypothesis is true.
B - There is a 90% chance that the confidence interval will include the true mean of the population.
C - There is a 10% chance of rejecting the null hypothesis when it is actually true.
D - There is a 90% chance of rejecting the null hypothesis when it is actually false.
C - There is a 10% chance of rejecting the null hypothesis when it is actually true.
The significance level specifies how different the observed sample mean has to be from the mean expected under the null hypothesis before we reject the null hypothesis. A significance level of 0.10 means that the observed sample mean is so different from the mean expected under the null hypothesis that it would only occur 10% of the time if the null hypothesis were true.
When performing a hypothesis test based on a 95% confidence level, what are the chances of making a type II error?
It is not possible to tell without more information.
