Question 5 If \( n-28, \bar{x}(x \)-bar \( )=39 \), and \( s=6 \), construct a confidence interval at a \( 80 \% \) confidence level. Assume the data came from a normally distributed population. Give your answers to one decimal place.

\( 1 \leftarrow \begin{array}{l}\text { Researchers conducted a study on using a chief executive officer's facial structure to predict a firm's financial } \\ \text { performance. The facial width-to-height ratio (WHR) for each in a sample of } 52 \text { CEOs at publicly traded firms was } \\ \text { determined. The sample resulted in } \bar{x}=1.55 \text { and } s=0.36 \text {. An analyst wants to predict the financial performance of a } \\ \text { firm based on the value of the true mean facial WHR of CEOs. The analyst wants to use the value of } \mu=2.1 \text {. Do yo } \\ \text { recommend he use this value? Conduct a test of hypothesis for } \mu \text { to help you answer the question. Specify all the } \\ \text { elements of the test, including } H_{0}, H_{a} \text {, test statistic, } p \text {-value, and your conclusion. Test at } \alpha=0.01 \text {. } \\ \text { What is the value of the test statistic? } \\ z=-11.02 \text { (Round to two decimal places as needed.) } \\ \text { Find the p-value. } \\ \text { p-value }=\square \text { (Round to three decimal places as needed.) }\end{array} \).

The annual rainfall in a certain region is approximately normally distributed with mean 42.6 inches and standard deviation 5.7 inches. Round answers to the nearest tenth of a percent. a) What percentage of years will have an annual rainfall of less than 44 inches? b) What percentage of years will have an annual rainfall of more than 40 inches? c) What percentage of years will have an annual rainfall of between 39 inches and 43 inches? Question Help: \( \quad \) Read Video

A random sample of 69 produced the summary statistics \( \bar{x}=0.326 \) and \( s^{2}=0.064 \). Complete parts a and \( b \). State and interpret the results of the test. A. Reject \( H_{0} \). There is insufficient evidence to indicate that the true population mean is less than 0.37 at \( \alpha=0.10 \). Bo not reject \( H_{0} \). There is sufficient evidence to indicate that the true population mean is less than 0.37 at \( \alpha=0.10 \). C. Reject \( H_{0} \). There is sufficient evidence to indicate that the true population mean is less than 0.37 at \( \alpha=0.10 \). Do not reject \( H_{0} \). Thefe is insufficient evidence to indicate that the true population mean is less than 0.37 at \( \alpha=0.10 \).

A random sample of 69 produced the summary statistics \( \bar{x}=0.326 \) and \( s^{2}=0.064 \). Complete parts a and \( \mathbf{b} \). b. Test the null hypothesis that \( \mu=0.37 \) against the alternative hypothesis that \( \mu \neq 0.37 \), using \( \alpha=0.10 \). What is the value of the test statistic? F=-1.44 (Round to two decimal places as needed.) Find the p-value. (Round to three decimal places as needed.)

A variable \( x \) is normally distributed with mean 21 and standard deviation 8 . Round your answers to the nearest hundredth as needed. a) Determine the \( z \)-score for \( x=27 \). \[ z=0.75 \] b) Determine the \( z \)-score for \( x=16 \). \[ z= \]