Questions and Answers

l. H0: p1=p2=p3, where p1 is the proportion of the sample of sophomores that responded yes, p2 is the proportion of the sample of juniors that responded yes, and p3 is the proportion of the sample of seniors that responded yes. ll. H0: There is an association between grade level and whether or not a student regularly recycles plastic bottles. lll. H0: There is no difference in the distribution of regular recyclers across the three grade levels.
A) II only
B) III only
C) I and II only
D) I and III only
E) I, II, and III

The corresponding p-value of 0.03 means that the probability of observing a test statistic of χ2=12.4 is 0.03, assuming the null hypothesis is true. Which of the following is a valid criticism of this interpretation of the p-value?
A) The null hypothesis can never be assumed to be true.
B) The null hypothesis is not stated.
C) The p-value is not the probability of observing 12.4 exactly.
D) The significance level is not stated.
E) The degrees of freedom are not stated.

If children from these countries exhibit top rounding in the same proportions, what is the expected count for Malay children who show top rounding?
A) 938
B) 951
C) 9
D) ((38)(51))/153
E) ((38)(9))/153

A quality control specialist tests samples of the seed being packaged and uses a chi-square goodness-of-fit test to see whether the proportions in the samples match what is claimed by the company. Which of the following best describes the null hypothesis and the alternative hypothesis for the test?
A) H0: p=0.20 Ha: p≠0.20
B) H0: pF=0.20, pB=0.20, pBG=0.20, pI=0.20, pNG=0.20 Ha: At least one of the proportions is different.
C) H0: pF=0.55, pB=0.22, pBG=0.10, pI=0.07, pNG=0.06 Ha: At least one of the proportions is different.
D) H0: All proportions are equally likely. Ha: All of the proportions are different.
E) H0: There is no association between the grass-seed types. Ha: There is an association between the grass-seed types.

Jimmy believes that the shuffle feature on his music player is malfunctioning by not playing songs that meet this distribution of music types. To test this, he listens to 100 songs randomly chosen when his player is in shuffle mode and records the number of songs in each category. Which inference procedure should he use to test whether or not the shuffle feature is working correctly?
A) A one-sample z-test for a population proportion
B) A two-sample z-test for a difference between population proportions
C) A chi-square goodness-of-fit test
D) A chi-square test for homogeneity
E) A matched pairs t-test for a mean difference

Ms. Harper knows that her students in a computing course can choose from one of three operating systems for the semester: Doors, Banana, or Duix. Ms. Harper wants to test the hypothesis that her students will select the operating systems in the same proportion as students in other computing courses at the university. She conducts a χ2 goodness-of-fit test and calculates χ2=3.79 with a corresponding p-value of 0.15. Which of the following is correct at a 5-percent level of significance?
A) Reject the null hypothesis, since 3.79>2.
B) Fail to reject the null hypothesis, since 3.79>2.
C) Reject the null hypothesis, since 0.15>0.05.
D) Fail to reject the null hypothesis, since 0.15>0.05.
E) Reject the null hypothesis, since 0.15<3.790.

A spinner made for a game of chance has 8 equally likely spaces. Alfonso records the result of a sample of 400 spins. Alfonso decides to calculate a chi-square test statistic for a goodness-of-fit test to see whether the spinner is fair. Which of the following is the appropriate null hypothesis?
A) H0
=0.125,p2=0.125,p3=0.125,p4=0.125,p5=0.125,p6=0.125,p7=0.125,p8=0.12
B) H0:H0: At least one proportion is different.
C) H0
=0.125
D) H0
≠0.125,p2≠0.125,p3≠0.125,p4≠0.125,p5≠0.125,p6≠0.125,p7≠0.125,p8≠0.125
E) H0
=0.08,p2=0.08,p3=0.08,p4=0.08,p5=0.08,p6=0.08,p7=0.08,p8=0.08

A certain type of legal proceeding has three possible outcomes: in favor of party A, in favor of party B, or not in favor of either party. The outcomes are expected to be 40 percent, 20 percent, and 40 percent, respectively. A random sample of 40 cases is selected from a certain judge to investigate whether the judge’s outcomes are consistent with the expected outcomes. A chi-square goodness-of-fit test is conducted, and the value of the chi-square test statistic is χ2=9.19 with a corresponding p-value of 0.01. Assuming the conditions for inference were met, which of the following is the correct interpretation of the p-value?
A) There is a 1 percent chance that the company’s claim is correct.
B) If the null hypothesis is true, there is a 1 percent chance that the company’s claim is correct.
C) If the null hypothesis is true, there is a 1 percent chance of obtaining a chi-square value of 9.19.
D) If the null hypothesis is true, there is a 1 percent chance of obtaining a chi-square value of at least 9.19.
E) There is a 1 percent chance of obtaining a chi-square value of at least 9.19.

Each student also identified which extracurricular activity (out of a total of 5 extra curricular activities) they were involved in. The calculated chi-square test statistic was 7.53 with a corresponding p-value of 0.4807. Based on this p-value, which of the following is the correct decision for the appropriate hypothesis test at the α=0.05 significance level?
A) Reject the null hypothesis. The test is statistically significant because a p-value of 0.4807 is greater than a significance level of 0.05.
B) Reject the null hypothesis. The test is statistically significant because a p-value of 0.4807 is less than the test statistic of 7.53.
C) Fail to reject the null hypothesis. The test is not statistically significant because a p-value of 0.4807 is greater than a significance level of 0.05.
D) Fail to reject the null hypothesis. The test is not statistically significant because a p-value of 0.4807 is less than the test statistic of 7.53.
E) Accept the null hypothesis. The test is not statistically significant because a p-value of 0.4807 is greater than a significance level of 0.05.

A regional highway uses 8 tollbooths that are open to all vehicles. A chi-square goodness-of-fit test using a significance level of α=0.05 was conducted to determine whether the tollbooths are all used in equal proportions. A chi-square value of χ2=19.1 was calculated with a corresponding p-value of 0.008. Which of the following is correct?
A) There is insufficient evidence to suggest that the tollbooths are not used in equal proportions.
B) There is insufficient evidence to suggest that the tollbooths are used in equal proportions.
C) There is sufficient evidence to suggest that the tollbooths are not used in equal proportions.
D) There is sufficient evidence to suggest that the tollbooths are used in equal proportions.
E) The tollbooths are used in equal proportion.