City officials will conduct a study of the proportion of vehicle owners among the neighborhood residents. The study, which was held 5 years ago, provided the result of 50%. Suppose that a random sample of size n = 20 with the obtained proportion 0.45 is used to decide if the proportion has increased for the whole neighborhood. Calculate the P-value using the appropriate test to analyze these data.
A) A large-sample z test can be used. 0.04

Question

City officials will conduct a study of the proportion of vehicle owners among the neighborhood residents. The study, which was held 5 years ago, provided the result of 50%. Suppose that a random sample of size n = 20 with the obtained proportion 0.45 is used to decide if the proportion has increased for the whole neighborhood. Calculate the P-value using the appropriate test to analyze these data. ​
A) A large-sample z test can be used. 0.04 < P-value < 0.06.
B) Both a randomization test for one proportion or a large-sample z test can be used. 0.04 < P-value < 0.06.
C) A large-sample z test, a randomization test for one proportion, or an exact binomial test for one proportion can be used. 0.06 < P-value < 0.08.
D) Both a randomization test for one proportion or an exact binomial test for one proportion can be used. 0.06 < P-value < 0.08.
E) Both a randomization test for one proportion or an exact binomial test for one proportion can be used. 0.09 < P-value < 0.1.

Quizplus · Accepted Answer

With a small sample size of 20, a large-sample z test is not appropriate. Therefore, options A and C are eliminated. Since the null hypothesis is that the proportion has not increased and the alternative hypothesis is that the proportion has increased, a one-tailed test can be used. Both a randomization test for one proportion or an exact binomial test for one proportion can be used in this case, making option D the correct choice. The P-value is between 0.06 and 0.08, based on the calculated test statistic and the appropriate distribution (either the binomial or sampling distribution).

City Officials Will Conduct a Study of the Proportion of Vehicle