In 1945, an organization asked 1440 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 757 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 \( \alpha=0.05 \) level of significance. What are the null and alternative hypotheses?

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

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.

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

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

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 \( =\square \)