AP Statistics - 10.2 - Comparing Two Means (FIX ANSWERS)

There are two common methods for measuring the

concentration of a pollutant in fish tissue. Do the two

methods differ, on average? You apply both methods

to each fish in a random sample of 18 carp and use

• the paired t test for $\mu_d$

• the one-sample z test for p

• the two-sample t test for $\mu_1-\mu_2$

• the two-sample z test for $p_1-p_2$

• none of these

A study of road rage asked random samples of 596 men and 523 women about their behavior while driving. Based on their answers, each person was assigned a road rage score on a scale of 0 to 20. The participants were chosen by random digit dialing of phone numbers. The researchers performed a test of the following hypotheses:
 $H_o:\ \mu_M=\mu_F\ versus\ H_a:\ \mu_M\ne\mu_F.$  
Which of the following describes a Type II error in the context of this study?

• Finding convincing evidence that the true means are different for males and females, when in reality the true means are the same

• Finding convincing evidence that the true means are different for males and females, when in reality the true means are different

• Not finding convincing evidence that the true means are different for males and females, when in reality the true means are the same

• Not finding convincing evidence that the true means are different for males and females, when in reality the true means are different

• Not finding convincing evidence that the true means are different for males and females, when in reality there is convincing evidence that the true means are different

A study of road rage asked random samples of 596 men and 523 women about their behavior while driving. Based on their answers, each person was assigned a road rage score on a scale of 0 to 20. The participants were chosen by random digit dialing of phone numbers. The researchers performed a test of the following hypotheses:
 $H_o:\ \mu_M=\mu_F\ versus\ H_a:\ \mu_M\ne\mu_F.$  
The P-value for the stated hypotheses is 0.002. Interpret this value in the context of this study.

• Assuming that the true mean road rage score is the same for males and females, there is a 0.002 probability of getting a difference in sample means.

• Assuming that the true mean road rage score is the same for males and females, there is a 0.002 probability of getting an observed difference at least as extreme as the observed difference.

• Assuming that the true mean road rage score is different for males and females, there is a 0.002 probability of getting an observed difference at least as extreme as the observed difference.

• Assuming that the true mean road rage score is the same for males and females, there is a 0.002 probability that the null hypothesis is true.

• Assuming that the true mean road rage score is the same for males and females, there is a 0.002 probability that the alternative hypothesis is true.

A study of road rage asked random samples of 596 men and 523 women about their behavior while driving. Based on their answers, each person was assigned a road rage score on a scale of 0 to 20. The participants were chosen by random digit dialing of phone numbers. The researchers performed a test of the following hypotheses:
 $H_o:\ \mu_M=\mu_F\$  
 $H_a:\ \mu_M\ne\mu_F$  
Given the P-value = 0.002 for a test with the stated hypotheses, which of the following must be true?

• A 90% confidence interval for $\mu_M-\mu_F$  will contain 0.

• A 95% confidence interval for $\mu_M-\mu_F$  will contain 0.

• A 99% confidence interval for $\mu_M-\mu_F$  will contain 0.

• A 99.9% confidence interval for $\mu_M-\mu_F$  will contain 0.

• It is impossible to determine whether any of these statements is true based only on the P-value.

(HT - Inf2) A guidance counselor is interested in comparing GPAs of students with home access to the Internet with students who do not have this access. She pulls the files of an SRS of ten students who do have home access to the Internet and an SRS of ten who do not, and proceeds to run a t-test to compare the mean GPAs of each group. Which of the following is a necessary assumption?

• The population standard deviations from each group are known.

• The population standard deviations from each group are unknown.

• The population standard deviations from each group are equal.

• The population of GPA scores from each group is normally distributed.

• The samples must be independent samples, and for each sample np and n(1 - p) must both be at least 10.

Tags

CCSS.HSS.ID.A.4

(HT - Inf4) A government statistician claims that the mean income level of families living in subsidized housing is $9,250 with a standard deviation of $2,575. A reporter plans to test this claim through interviews with a random sample of 50 families. If she finds a sample mean more than $500 different from the claimed $9,250, she will dispute the statistician's claim. What is the probability that the reporter will mistakenly reject a true claim?

• .043

• .085

• .170

• .830

• .915

Tags

CCSS.HSS.IC.B.4