Question

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In 1945, an organization asked 1448 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 766 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 a = 0.05 level of significance. What are the null and alternative hypotheses? Ho vversus Hy (Type integers or decimals.) Determine the test statistic, 20- zo - (Round to two decimal places as needed.) Use technology to determine the P-value for the test statistic. The P-value is (Round to three decimal places as needed.) What is the correct conclusion at the a= 0.05 level of significance? Since the P-value is than the level of significance, the null hypothesis. There 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

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p = 0.5
Alternative Hypothesis, Ha: p > 0.5

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.529005524861878 - 0.5)/sqrt(0.5*(1-0.5)/1448)
z = 2.21

P-value Approach
P-value = 0.014
As P-value < 0.05, reject the null hypothesis.

Since the p value is less than the significance, reject the null hypothesis. There is sufficient evidence