Consider the following hypotheses:

$$\begin{aligned} &H_0: p=0.32 \\ &H_A: p \neq 0.32 \end{aligned}$$

Calculate the $p$-value based on the following sample information a. $x=20 ; n=66$

b. $x=100 ; n=264$

c. $\bar{p}=0.40 ; \mathrm{n}=40$

d. $\bar{p}=0.38 ; n=180$

In order to conduct a hypothesis test for the population proportion, you sample 320 observations that result in 128 successes. Conduct the following tests at $\alpha=0.05$.

b. $H_0: p=0.45 ; H_A: p \neq 0.45$

In order to conduct a hypothesis test for the population proportion, you sample 320 observations that result in 128 successes. Conduct the following tests at $\alpha=0.05$.

a. $H_0: p \geq 0.45 ; H_A: p<0.45$

b. $H_0: p=0.45 ; H_A: p \neq 0.45$

The manager of a large manufacturing firm is considering switching to new and expensive software that promises to reduce its assembly costs. Before purchasing the software, the manager wants to conduct a hypothesis test to determine if the new software does reduce its assembly costs.

a. Would the manager of the manufacturing firm be more concerned about a Type I error or a Type ll error? Explain.

b. Would the software company be more concerned about a Type I error or a Type II error? Explain.

The manager of a newly opened Target store wants to estimate the average expenditure of his customers. From a preselected sample, the standard deviation was determined to be $\$ 18$. The manager would like to construct the $95 \%$ confidence interval for the mean customer expenditure.

a. Find the appropriate sample size necessary to achieve a margin of error of $\$ 5$.

b. Find the appropriate sample size necessary to achieve a margin of error of $\$ 3$.

A realtor in Mission Viejo, California, believes that the average price of a house is more than $\$ 500,000$.

b. The data accompanying this exercise show house prices. (Data are in $\$ 1,000 \mathrm{~s}$.) Assume the population standard deviation is $\$ 100$ (in $\$ 1,000$ s). What is the value of the test statistic and the $p$-value?

A realtor in Mission Viejo, California, believes that the average price of a house is more than 500,000$.

a. State the null and the alternative hypotheses for the test.

b. The data accompanying this exercise show house prices. (Data are in 1,000$ s.) Use Excel's Z.TEST function to calculate the $p$-value. Assume the population standard deviation is $\$ 100$ (in 1,000$s).

c. At$\alpha=0.05$, what is the conclusion to the test? Is the realtor's claim supported by the data?

A realtor in Mission Viejo, California, believes that the average price of a house is more than $\$ 500,000$.

c. At $\alpha=0.05$, what is the conclusion to the test? Is the realtor's claim supported by the data?

A realtor in Mission Viejo, California, believes that the average price of a house is more than $\$ 500,000$.

a. State the null and the altemative hypotheses for the test.

b. The data accompanying this exercise show house prices. (Data are in $\$ 1,000 \mathrm{~s}$.) Assume the population standard deviation is $\$ 100$ (in $\$ 1,000$ s). What is the value of the test statistic and the $p$-value?

c. At $\alpha=0.05$, what is the conclusion to the test? Is the realtor's claim supported by the data?

The manager of a newly opened Target store wants to estimate the average expenditure of his customers. From a preselected sample, the standard deviation was determined to be $\$ 18$. The manager would like to construct the $95 \%$ confidence interval for the mean customer expenditure.

a. Find the appropriate sample size necessary to achieve a margin of error of 5$.

b. Find the appropriate sample size necessary to achieve a margin of error of 3$. |

A realtor in Mission Viejo, California, believes that the median price of a house is more than $\$ 500,000$.

a. Specify the competing hypotheses for the test.

b. Using the $\boldsymbol{M} \boldsymbol{V}_{-}$Houses data, calculate the value of the test statistic. Assume the normal approximation for $T$.

c. Calculate the $p$-value.

d. At the $5 \%$ significance level, is the realtor's claim supported by the data?

An economist reports that 560 out of a sample of 1,200 middle-income American households actively participate in the stock market.

a. Construct the 90% confidence interval for the proportion of middle-income Americans who actively participate in the stock market.

b. Can we conclude that the proportion of middleincome Americans who actively participate in the stock market is not 50% ?

Use the sample values given in the Exercise to construct a $95 \%$ confidence interval estimate of the population mean. Assume that the population has a normal distribution.

Suppose the 95% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$36,080, $43,920]. The population standard deviation used for the analysis is known to be 12,000$.

a. What is the point estimate of the mean salary for all college graduates in this town?

b. Determine the sample size used for the analysis.