In 1945, an organization asked 1467 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 763 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. \( \mathrm{H}_{0}: \mathrm{p}=0.5 \) versus \( \mathrm{H}_{1}: \quad \mathrm{p} \) (Type integers or decimals.) Determine the test statistic, \( \mathrm{z}_{0} \). \( \mathrm{z}_{0}=1.55 \) (Round to two decimal places as needed.) Use technology to determine the P-value for the test statistic. The P -value is \( \square \). (Round to three 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

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 \( =\square \)

SAT scores are normally distributed with a mean of 1,500 and a standard deviation of 300 . An administrator at a college is interested in estimating the average SAT score of first-year students. If the administrator would like to limit the margin of error of the \( 96 \% \) confidence interval to 25 points, how many students should the administrator sample? Make sure to give a whole number answer.

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.

pose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.6 and a standard deviation of 0.42 cribe where approximately \( 95 \% \) of grade point averages lie. swer \[ \text { below } 1.76 \text { and above } 3.44 \] between 1.76 and 3.18 and above 3.02