Question

Suppose a random sample of 100 observations from a binomial population gives a value of p = 0.45 and you wish to test the null hypothesis that the population parameter p is equal to 0.40 against the alternative hypothesis that p is greater than 0.40. Complete parts a through c. a. Noting that p = 0.45, what does your intuition tell you? Does the value of p appear to contradict the null hypothesis? O A. Yes, because p satisfies Hg:p>0.40 and is not very close to 0.40. O B. No, because p is very close to 0.40. OC. Yes, because p satisfies Hg:p>0.40 and is very close to 0.40. OD. Yes, because p is very close to 0.40. b. Use the large-sample z-test to test Ho: p=0.40 against the alternative hypothesis, Hg:p>0.40. Use a = 0.05. If a = 0.05, find the rejection region for the test. Choose the correct answer below. O A. z< -1.96 OC. Z> 1.645 O E. z< -1.645 OB. 25 -1.645 or z > 1.645 OD. z>1.96 OF. Z< -1.96 or z > 1.96 Calculate the value of the test statistic. z= (Round to two decimal places as needed.) What is the conclusion of the test? O A. Reject the null hypothesis because the test statistic is not in the rejection region. O B. Do not reject the null hypothesis because the test statistic is not in the rejection region. O C. Reject the null hypothesis because the test statistic is in the rejection region. OD. Do not reject the null hypothesis because the test statistic is in the rejection region. c. Find and interpret the observed significance level of the test conducted in part b. The p-value of the test is (Round to three decimal places as needed.) What does this p-value mean? O A. Assuming p=0.45, the p-value is the probability that is greater than 0.40 for a random sample of 100 observations. OB. Assuming p = 0.40, the p-value is the probability that is greater than 0.40 for a random sample of 100 observations. OC. Assuming p = 0.45, the p-value is the probability that p is greater than 0.45 for a random sample of 100 observations. O D. Assuming p=0.40, the p-value is the probability that is greater than 0.45 for a random sample of 100 observations.

Answer 1

a)
Option C

b)
Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.645.
Hence reject H0 if z > 1.645

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.45 - 0.4)/sqrt(0.4*(1-0.4)/100)
z = 1.02

Do not reject H0
option B

c)
P-value Approach
P-value = 0.1539
As P-value >= 0.05, fail to reject null hypothesis.

option C