Ch. 8 Test Review CPA Stats

A lightbulb company claims that their lightbulbs last 1000 hours. To test this claim, a consumer selects a random sample of 20 lightbulbs manufactured by the company. The consumer turned on the lightbulbs and recorded the time it took until the lightbulbs burned out. A significance test is performed using the following hypotheses at the 5% significance level:

Ho: mu = 1000 vs. Ha: mu < 1000

where µ = the mean time until burn-out for all lightbulbs from this company. Which of the following describes a Type I error in this setting?

• The consumer does not find convincing evidence that the lightbulbs last, on average, 1000 hours, when it fact the P-value of the test was not small enough to reject the null hypothesis.

• The consumer does not find convincing evidence that the lightbulbs last, on average, 1000 hours, when it fact the P-value of the test was small enough to reject the null hypothesis.

• The consumer finds convincing evidence that the lightbulbs last, on average, 1000 hours, when it fact the lightbulbs last less than 1000 hours, on average.

• The consumer advocate finds convincing evidence that the lightbulbs last, on average, less than 1000 hours, when it fact the lightbulbs last 1000 hours, on average.

The parent association at a local high school believes that the amount of time spent on homework by students at the school, on average, is more than the school’s policy of an average of 30 minutes of homework per class. To test this claim, the administrators selected a random sample of 50 students, calculated the amount of time each student spent on homework per class, and tested the hypotheses listed here:

Ho: mu = 30 vs. Ha: mu > 30

Where = the mean number of minutes spent on homework, per class, for all students in the school. The mean number of minutes spent on homework, per class, for the students in the sample was minutes and the standard deviation was minutes. The administrators performed a significance test and obtained a P-value of 0.0012. Based on the P-value, what conclusion would you make?

• The P-value is small, so we fail to reject H0. We do not have convincing evidence that the mean amount of time spent is more than 30 minutes per class.

• The P-value is small, so we fail to reject H0. We have convincing evidence that the mean amount of time spent is more than 30 minutes per class.

• The P-value is small, so we reject H0. We do not have convincing evidence that the mean amount of time spent is more than 30 minutes per class.

• The P-value is small, so we reject H0. We have convincing evidence that the mean amount of time spent is more than 30 minutes per class.

Because of the expense of running a campaign, a potential candidate for mayor will only decide to run for mayor if there is more than 40% initial support for him. To test the initial support, the candidate’s election committee selects a random sample of 200 voters and asks each person if they would vote for this candidate over the current mayor. A significance test is performed using the following hypotheses at the 10% significance level:

Ho: p = 0.40 vs. Ha: p > 0.40

where p = the true proportion of voters that would vote for this candidate over the current mayor. Which of the following describes a consequence of a Type II error in this setting?

• Thinking that there is enough support, but the candidate still decides not to run for office.

• Thinking that there is not enough support, but the candidate still decides to run for office.

• Thinking that there is not enough support, so the candidate decides not to run for office. The candidate saves money, but might have won because the initial support is more than 40%.

• Thinking that there is enough support, so the candidate decides to run for office. This is a waste of money because the initial support is not more than 40%.

A fast-food restaurant manager wants to know if more than 60% of her customers that request a water cup actually fill the cup with soda instead of water. The manager would like to carry out a test at the a = 0.10 significance level of

Ho: p = 0.60 vs. Ha: p > 0.60

where p = the true proportion of customers that fill a water cup with soda rather than water. During the next month, the manager collected data from a random sample of 90 customers that ask for a water cup by observing that 63 of the customers filled the water cup with soda. Which of the following is the standardized test statistic for this hypothesis test?

• 1.9365

• 2.0702

• – 1.9365

• – 2.0702

Suppose that you want to perform a test of

Ho: p = 0.75 vs. Ha: p > 0.75

An SRS of size 250 from the population of interest yields 200 successes. Which of the following is closest to the P-value for this hypothesis test?

• 0.0241

• 0.0339

• 0.9661

• 0.9759

An elementary school administrator wanted to see if the students were being assigned more than the maximum of 60 minutes of homework each night. She conducted a significance test at the a = 0.05 significance level of H0: m = 60 versus Ha: m > 60, where m = the true mean time spent on homework each night for all students. The administrator selected a random sample of 15 of students and calculated the standardized test statistic to be t = 2.137. Using Table B, which of the following is the range the P-value is between for the significance test the school administrator wants to perform? Assume that the conditions for carrying out the test are met.

• The P-value is between 0.01 and 0.02.

• The P-value is between 0.02 and 0.025.

• The P-value is between 0.025 and 0.05.

• The P-value is between 0.05 and 0.10.

Which of the following best describes a Type I error?

• The null is true, but we mistakenly reject it.
• The null is false and we reject it.
• The null is false, but we fail to reject it.
• The null is true but we fail to reject it.

Tags

CCSS.HSS.MD.B.7

The null hypothesis always contains a(an):

• < or >
• =
• >
• = or >

When p-value is greater than alpha we:

• Accept Ho
• Accept Ha
• Fail to reject Ho
• Reject Ho

Which of the following best describes a Type II error?

• The null is true but we mistakenly reject it.

• The null is false but we mistakenly reject it.

• The null is false but we fail to reject it.

• The null is true but we fail to reject it.

Tags

CCSS.HSS.MD.B.7