Copy of MCQ- Significance Test for Proportions

A researcher is conducting a study of charitable donations by surveying a simple random sample of households in a certain city. The researcher wants to determine whether there is convincing statistical evidence that more than 50 percent of households in the city gave a charitable donation in the past year. Let p represent the proportion of all households in the city that gave a charitable donation in the past year. Which of the following are appropriate hypotheses for the researcher?

• H0: p = 0.5 and Ha: p > 0.5

• H0: p = 0.5 and Ha: p ≠ 0.5

• H0: p = 0.5 and Ha: p < 0.5

• H0: p > 0.5 and Ha: p ≠ 0.5

• H0: p > 0.5 and Ha: p = 0.5

A national newspaper reported that 40 percent of high school students engage in community service activities. A school administrator wondered whether the proportion of high school students at the administrator’s school who engage in community service activities is less than 40 percent. The administrator selected a random sample of 100 students, and 36 responded that they do engage in community service activities. The conditions for inference were met, and an appropriate hypothesis test resulted in a p-value of 0.207. Which of the following is a correct interpretation of this p-value?

• The probability that a randomly selected student at this high school engages in community service activities is 0.207.

• The probability is 0.40 that less than 20.7 percent of students at this high school engage in community service activities.

• The probability is 0.207 that less than 40 percent of students at this high school engage in community service activities.

• If the proportion of all students at the school who engage in community service activities is 0.4, the probability of observing 36 or fewer in a random sample of 100 students who engage in community service activities is 0.207.

• If the proportion of all students at the school who engage in community service activities is 0.36, the probability of obtaining 40 or fewer in a random sample of 100 who engage in community service activities is 0.207.

A survey of a random sample of 1,045 young adults found that 60 percent do not have a landline telephone number. A hypothesis test will be used to determine whether the data provide convincing statistical evidence that more than 50 percent of all young adults do not have a landline telephone number. Which of the following is the test statistic for the appropriate test?

• Z = (0.60 - 0.50) / sqrt((0.50 * 0.50) / 1045)

• Z = (0.50 - 0.60) / sqrt((0.60 * 0.40) / 1045)

• Z = (0.60 - 0.50) / sqrt((0.60 * 0.40) / 1045)

• Z = (0.50 - 0.60) / sqrt((0.50 * 0.50) / 1045)

What is the correct interval for the proportion?

• 0.50 – 0.60

• 0.60 – 0.50

Tags

CCSS.HSS.IC.B.4

• Yes, because the sample estimate of 0.04 is greater than the company specification of 0.03.

Tags

CCSS.HSS.IC.B.4

• Yes, because 0.56 > 0.53.

• Yes, because a reasonable interval for the proportion is 0.56 ± 0.283.

• Yes, because 0.56 - 0.53 = 0.03 and 0.03 < 0.05.

• No, because 0.283 < 0.53.

• No, because 0.283 > 0.05.

Tags

CCSS.HSS.IC.B.4

A study reported that 14 percent of cars registered in 2015 had a manual transmission. An automotive researcher collected data on cars registered in 2021 to investigate whether the proportion of registered cars with a manual transmission is less than 0.14. The researcher took a random sample of 150 cars registered in 2021 and found 18 of the cars had a manual transmission. After ensuring the conditions for inference were met, the researcher conducted an appropriate hypothesis test and calculated a p-value of 0.24. At the 5 percent level of significance, which of the following conclusions should be made?

• (A) The null hypothesis should be rejected. There is significant evidence that the population proportion of registered cars with a manual transmission in 2021 is less than 0.14.

• (B) The null hypothesis should be rejected. There is not significant evidence that the population proportion of registered cars with a manual transmission in 2021 is less than 0.14.

• (C) The null hypothesis should not be rejected. There is significant evidence that the population proportion of registered cars with a manual transmission in 2021 is not less than 0.14.

• (D) The null hypothesis should not be rejected. There is significant evidence that the population proportion of registered cars with a manual transmission in 2021 is equal to 0.14.

• (E) The null hypothesis should not be rejected. There is not significant evidence that the population proportion of registered cars with a manual transmission in 2021 is less than 0.14.

A one-sided hypothesis test is to be performed with a significance level of 0.05. Suppose that the null hypothesis is false. If a significance level of 0.01 were to be used instead of a significance level of 0.05, which of the following would be true?

• Neither the probability of a Type II error nor the power of the test would change.

• Both the probability of a Type II error and the power of the test would decrease.

• Both the probability of a Type II error and the power of the test would increase.

• The probability of a Type II error would decrease and the power of the test would increase.

• The probability of a Type II error would increase and the power of the test would decrease.

Which of the following best describes the power of the test?

• The probability of issuing a ticket to a driver who is speeding

• The probability of issuing a ticket to a driver who is not speeding

• The probability of not issuing a ticket to a driver who is speeding

• The probability of not issuing a ticket to a driver who is not speeding

• The probability that the motion detector is working correctly

Tags

CCSS.HSS.MD.A.2

A statistical test involves the following null and alternative hypotheses. H0 : μ = 64 Ha : μ > 64 Which of the following describes a Type II error?

• Failing to reject the null hypothesis when the population mean is 64

• Failing to reject the null hypothesis when the population mean is greater than 64

• Rejecting the null hypothesis when the population mean is 64

• Rejecting the null hypothesis when the population mean is greater than 64

• Failing to reject the null hypothesis when the p-value is less than the significance level