A sample size of n= 20 is a simple random sample selected from a normally distributed
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Answer:
We conclude that majority of the citizens does not feel the country could develop a way to protect itself from atomic bombs.
Step-by-step explanation:
We are given that an organization asked 1403 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 737 responding yes.
We have to conduct a test to determine that a majority of the citizens feel the country could develop a way to protect itself from atomic bombs in 1945.
<u><em>Let p = percentage of citizens feel the country could develop a way to protect itself from atomic bombs in 1945.</em></u>
SO, Null Hypothesis, : p
50% {means that majority of the citizens does not feel the country could develop a way to protect itself from atomic bombs}
Alternate Hypothesis, : p > 50% {means that majority of the citizens feel the country could develop a way to protect itself from atomic bombs}
The test statistics that will be used here is <u>One-sample z proportion</u> <u>statistics</u>;
T.S. = ~ N(0,1)
where, = proportion of citizens responding yes in a sample of 1403 citizens =
n = sample of citizens = 1403
So, <u><em>test statistics</em></u> =
= 1.898
The value of the test statistics is 1.898.
<em>Now at 1% significance level, the z table gives critical value of 2.3263 for right-tailed test. Since our test statistics is less than the critical value of z as 1.898 < 2.3263, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which </em><em><u>we fail to reject our null hypothesis</u></em><em>.</em>
Therefore, we conclude that majority of the citizens does not feel the country could develop a way to protect itself from atomic bombs.