This Question: 4 pts 25 of 25 (24 complete) This Test: 100 pts possible In 1945,

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This Question: 4 pts 25 of 25 (24 complete) This Test: 100 pts possible In 1945, an organization asked 1516 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 788 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 0.05 level of significance. distribution table f her sta whar are ne nuil and altmative hyponeses Type integers or decimals. Do not round.) Deterrmine the test statistic, Zo ,-! (Round to two decimal places as needed.) Determine the critical value(s). Select the correct choice below and fill in the answer box to complete your choice (Round to two decimal places as needed.) A. The critical values are ± O B. The critical value is What is the correct conclusion at the = 0.05 level of significance? Since the test statistic is protect itself from atomic bombs. | than the critical value | the null hypothesis. There | sufficient evidence to conclude that the majority of the citizens feel the country could develop a way to Click to select your answer(s).

Explanation / Answer

n = 1516
and
p = 788/1516 = 0.52

we shall have to test the hypothesis that

H0: proportion is not greater than 0.5
H1: proportion is greater than 0.5

Zstat is
Z = (p-p0)/sqrt(p0*(1-p0)/n)

z = (0.52-0.5)/sqrt(0.5*(1-0.5)/1516) = 1.557

the critical value for the test is

please note that this is a 1 tail test

we see the critical value is -1.6449

as the test statisitc is greater than critical value hence we reject the null hypothesis in favor of alternate hypothesis . There is sufficient evidence

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