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.)

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

Score on last try: 0 of 1 pts. See Details for more. \( > \) Next question Assume that \( z \)-scores are normally distributed with a mean of 0 and a standard deviation of 1 . If \( P(-b<z<b)=0.6956 \), 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 \( =\square \)

\( n-1=35-1=34 \) \( p \)-value \( <0.01 \) - Step 6: Make a decision to reject or not reject the null hypothesis. Write in non-techni terms a final conclusion about the claim. 'd reject the nurl nypo thesis

You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.05 \) \[ \begin{array}{l}H_{o}: \mu=72.3 \\ H_{a}: \mu \neq 72.3\end{array} \] You believe the population is normally distributed, but you do not know the standard deviation. You obta a sample of size \( n=5 \) with mean \( M=78.2 \) and a standard deviation of \( S D=18.8 \). What is the p-value for this sample? (Report answer accurate to four decimal places.) -value \( =\square \)