Consider the following hypotheses:

$$\begin{aligned} &H_0: \mu \leq 210 \\ &H_A: \mu>210 \end{aligned}$$

Find the $p$-value for this test based on the following sample information.

b. $\bar{X}=216 ; s=26 ; n=80$

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

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 $\$ 500,000$.

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 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?

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?

Rates on 30-year fixed mortgages continue to be at historic lows (Chron Business News, September 23, 2010). According to Freddie Mac, the average rate for 30 -year fixed loans for the week was $4.37 \%$. An economist wants to test if there is any change in the mortgage rates in the following week. She searches the Internet for 30-year fixed loans in the following week and reports the rates offered by seven banks as $4.25 \%, 4.125 \%, 4.375 \%$, $4.50 \%, 4.75 \%, 4.375 \%$, and $4.875 \%$. Assume that rates are normally distributed.

a. State the hypotheses to test if the average mortgage rate differs from $4.37 \%$.

b. Calculate the value of the test statistic and the $p$-value.

c. At the $5 \%$ significance level, does the average mortgage rate differ from $4.37 \%$ ? Explain

Rates on 30-year fixed mortgages continue to be at historic lows (Chron Business News, September 23,2010 ). According to Freddie Mac, the average rate for 30-year fixed loans or the week was $4.37 \%$. An economist wants to test if there is any change in the mortgage rates in the following week. She searches the Internet for 30 -year fixed loans in the ollowing week and reports the rates offered by seven banks as $4.25 \%, 4.125 \%, 4.375 \%$, $4.50 \%, 4.75 \%, 4.375 \%$, and $4.875 \%$. Assume that rates are normally distributed.

At the $5 \%$ significance level, does the average mortgage rate differ from $4.37 \%$ ? Explain.

Rates on 30-year fixed mortgages continue to be at historic lows (Chron Business News, September 23,2010 ). According to Freddie Mac, the average rate for 30-year fixed loans or the week was $4.37 \%$. An economist wants to test if there is any change in the mortgage rates in the following week. She searches the Internet for 30 -year fixed loans in the ollowing week and reports the rates offered by seven banks as $4.25 \%, 4.125 \%, 4.375 \%$, $4.50 \%, 4.75 \%, 4.375 \%$, and $4.875 \%$. Assume that rates are normally distributed.

Calculate the value of the test statistic and the $p$-value.

A polygraph (lie detector) is an instrument used to determine if an individual is telling the truth. These tests are considered to be $95 \%$ reliable. In other words, if an individual lies, there is a $0.95$ probability that the test will detect a lie. Let there also be a $0.005$ probability that the test erroneously detects a lie even when the individual is actually telling the truth. Consider the null hypothesis, "the individual is telling the truth," to answer the following questions.

a. What is the probability of a Type I error?

b. What is the probability of a Type II error?

c. Discuss the consequences of Type I and Type II errors.

d. What is wrong with the statement, "I can prove that the individual is telling the truth on the basis of the polygraph result."

A polygraph (lie detector) is an instrument used to determine if an individual is telling the truth. These tests are considered to be $95 \%$ reliable. In other words, if an individual lies, there is a $0.95$ probability that the test will detect a lie. Let there also be a $0.005$ probability that the test erroneously detects a lie even when the individual is actually telling the truth. Consider the null hypothesis, "the individual is telling the truth." to answer the following questions.

a. What is the probability of a Type I error?

b. What is the probability of a Type II error?

c. What are the consequences of Type I and Type II errors?

d. What is wrong with the statement, "I can prove that the individual is telling the truth on the basis of the polygraph result"?

A polygraph (lie detector) is an instrument used to determine if an individual is telling the truth. These tests are considered to be $95 \%$ reliable. In other words, if an individual lies, there is a $0.95$ probability that the test will detect a lie. Let there also be a $0.005$ probability that the test erroneously detects a lie even when the individual is actually telling the truth. Consider the null hypothesis, "the individual is telling the truth," to answer the following questions. b. What is the probability of a Type II error?

A polygraph (lie detector) is an instrument used to determine if an individual is telling the truth. These tests are considered to be $95 \%$ reliable. In other words, if an individual lies, there is a $0.95$ probability that the test will detect a lie. Let there also be a $0.005$ probability that the test erroneously detects a lie even when the individual is actually telling the truth. Consider the null hypothesis, "the individual is telling the truth," to answer the following questions.

c. What are the consequences of Type I and Type II errors?