In 1945, an organization asked 1495 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 793 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 \( \alpha=0.1 \) level of significance. What are the null and alternative hypotheses? Determine the test statistic, \( \mathrm{z}_{0} \). \( \mathrm{z}_{0}=\square \) (Round to two decimal places as needed.)

Question 12 Assume that \( z \)-scores are normally distributed with a mean of 0 and a standard deviation of 1. \( b=\square<b<b)=0.747 \), find \( b \). Submit Question

Assume that \( z \)-scores are normally distributed with a mean of 0 and a standard deviation of 1 . If \( P(-b<z<b)=0.7944 \), find \( b \). \( b=\square \) Submit Question

5 The mean age for first 13 voters at Zwide Voting Station, is 40 and the standard deviation is 5. Comment by refering to the standard deviations on how the ages at Zwide Station compare to those at Dingiswayo Station.

Find the range of the following data set. Assume the data set is a sample.

You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.10 \). \[ \begin{array}{l}H_{o}: \mu=51.7 \\ H_{a}: \mu<51.7\end{array} \] You believe the population is normally distributed, but you do not know the standard deviation. You obt: a sample of size \( n=23 \) with mean \( M=45.5 \) and a standard deviation of \( S D=14.1 \). What is the p -value for this sample? (Report answer accurate to four decimal places.) p -value \( =\square \)