Question

In 1945, an organization asked 1432 randomly sampled American​ citizens, "Do you think we can develop a way to protect ourselves from atomic bombs in case others tried to use them against​ us?" with 742 responding yes. Did a majority of the citizens feel the country could develop a way to protect itself from atomic bombs in 1945? Use the α=0.05 level of significance.

(A) What are the null and alternative​ hypotheses?

(B) Determine the test statistic, z0.

z0 = (BLANK)

(C) Determine the critical​ value(s). Select the correct choice below and fill in the answer box to complete your choice.

a - The critical value is (BLANK)

OR

b - The critical values are +/-(BLANK)

(D) What is the correct conclusion at the α=0.05 level of​ significance?

Since the test statistic is (Greater/Less) than the critical value, (do not reject/reject) the null hypothesis. There (is/is not) sufficient evidence to conclude that the majority of the citizens feel the country could develop a way to protect itself from atomic bombs.

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

A)

Null hypothesis: P = 0.50
Alternative hypothesis: P > 0.50

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).

S.D = 0.013213
B)

z = (p - P) / S.D

z = 1.37

C)

z_Critical = + 1.645

Rejection region is z > + 1.645

where P is the hypothesised value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

D) Interpret results. Since the z-value (1.37) does not lies in the rejection region, hence failed to reject the null hypothesis.

Since the test statistic is less than the critical value, do not the null hypothesis. There is not sufficient evidence to conclude that the majority of the citizens feel the country could develop a way to protect itself from atomic bombs.