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?

Each month a brokerage house studies various companies and rates each company's stock as being either "low risk" or "moderate to high risk." In a recent report, the brokerage house summarized its findings about $15$ aerospace companies and $25$ food retailers in the following table:

$$\begin{array}{lcc} & & \text { Moderate to } \\ \text { Company Type } & \text { Low Risk } & \text { High Risk } \\ \text { Aerospace company } & 6 & 9 \\ \text { Food retailer } & 15 & 10\end{array}$$

If we randomly select one of the total of $40$ companies, find

The probability that the company's stock is "moderate to high risk."

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?

A realtor in Mission Viejo, California, believes that the median price of a house is more than $\$ 500,000$. The accompanying data is in $\$ 1,000$ s.

a. Specify the competing hypotheses for the test.

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

A realtor wants to estimate the mean price of houses in Mission Viejo, California. She collects a sample of 36 recent house sales, a portion of which is shown in the accompanying table. Assume that the population standard deviation is 100 (in $\$ 1,000 \mathrm{~s}$ ). Construct and interpret 95 % and 98 % confidence intervals for the mean price of all houses in Mission Viejo, CA.

$$\begin{array}{|c|} \hline \text { Prices (in \$1,000s) } \\ \hline 430 \\ \hline 520 \\ \hline \vdots \\ \hline 430 \\ \hline \end{array}$$

The gravitational attraction between two objects is determined by the mass of the two objects and the

a. distance between the objects.

b. weight of the objects.

c. diameter of the objects.

d. density of the objects.

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?

Radon is a colorless, odorless gas that is naturally released by rocks and soils and may concentrate in tightly closed houses. Because radon is slightly radioactive, there is some concern that it may be a health hazard. Radon detectors are sold to homeowners worried about this risk, but the detectors may be inaccurate. University researchers placed a random sample of 11 detectors in a chamber where they were exposed to 105 picocuries per liter of radon over 3 days. A graph of the radon readings from the 11 detectors shows no strong skewness or outliers. The mean reading is 104.82 and the standard deviation of the readings is 9.54. Is there convincing evidence at the 10% level that the mean reading differs from the true value 105?

Customers at Costco spend an average of $\$ 130$ per trip (The Wall Street Journal, October 6,2010 ). One of Costco's rivals would like to determine whether its customers spend more per trip. A survey of the receipts of 25 customers found that the sample mean was $\$ 135.25$. Assume that the population standard deviation is $\$ 10.50$ and that spending follows a normal distribution.

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

Education reform is one of the most hotly debated subjects on both state and national policy makers' list of socioeconomic topics. Consider a linear regression model that relates school expenditures and family background to student performance in Massachusetts using 224 school districts. The response variable is the mean score on the MCAS (Massachusetts Comprehensive Assessment System) exam given in May 1998 to 10th graders. Four explanatory variables are used: (1) STR is the student-to-teacher ratio in $\%$, (2) TSAL is the average teacher's salary in $\$ 1,000 \mathrm{~s},(3) \mathbb{N C}$ is the median household income in $\$ 1,000$ s, and (4) SGL is the percentage of single-parent households. A portion of the data is shown in the accompanying table.

$$\begin{array}{|c|c|c|c|c|} \hline \text { Score } & \text { STR } & \text { TSAL } & \text { INC } & \text { SGL } \\ \hline 227.00 & 19.00 & 44.01 & 48.89 & 4.70 \\ \hline 230.67 & 17.90 & 40.17 & 43.91 & 4.60 \\ \hline \vdots & \vdots & \vdots & \vdots & \vdots \\ \hline 230.67 & 19.20 & 44.79 & 47.64 & 5.10 \\ \hline \end{array}$$

c. What is the predicted score if $\mathrm{STR}=18, \mathrm{TSAL}=50, \mathrm{INC}=60, \mathrm{SGL}=5$ ?

According to a report on workforce diversity, about $60 \%$ of the employees in high-tech firms in Silicon Valley are white and about $20 \%$ are Asian (wuw.money.cnn.com, November 9, 2011). Women, along with blacks and Latinos, are highly underrepresented. Just about $30 \%$ of all employees are women, with blacks and Latinos accounting for only about $15 \%$ of the workforce. Tara Jones is a recent college graduate, working for a large high-tech firm in Silicon Valley. She wants to determine if her firm faces the same diversity as in the report. She collects gender and ethnicity information on $50$ employees in her firm. A portion of the data is shown in the accompanying table.

$$\begin{array}{|l|l|} \hline \text { Cender } & \text { Ethnicity } \\ \hline \text { Female } & \text { White } \\ \hline \text { Male } & \text { White } \\ \hline \vdots & \vdots \\ \hline \text { Male } & \text { Nonwhite } \\ \hline \end{array}$$

b. At the $5 \%$ level of significance, determine if the proportion of whites in Tara's firm is more than $0.50$.

Radon is a colorless, odorless gas that is naturally released by rocks and soils and may concentrate in tightly closed houses. It is slightly radioactive, so there is some concern that it may pose a health hazard. Radon detectors are sold to homeowners, but the detectors may be inaccurate. University researchers placed a random sample of 11 detectors in a chamber and exposed them to 105 picocuries per liter of radon over 3 days. A graph of the radon readings from the 11 detectors shows no strong skewness or outliers. The 90% confidence interval for the true mean reading is 99.61 to 110.03. What conclusion would you make for a test at the $\alpha=0.10$ significance level of $H_{0}: \mu=105$ versus $H_{a}: \mu \neq 105,$ where $\mu$ is the true mean reading in the population of radon detectors? Explain.

Construct the null and the alternative hypotheses for the following claims:

a. "I am going to get the majority of the votes to win this election."

b. "I suspect that your 10 -inch pizzas are, on average, less than 10 inches in size."

c. "I will have to fine the company since its tablets do not contain an average of $250 \mathrm{mg}$ of ibuprofen as advertised."

(a) State the null hypothesis and the alternate hypothesis. (b) State the decision rule. (c) Compute the value of the test statistic. (d) What is your decision regarding

$$H_0?$$

(e) What is the p-value? Interpret it. The manufacturer of the X-15 steel-belted radial truck tire claims that the mean mileage the tire can be driven before the tread wears out is 60,000 miles. Assume the mileage wear follows the normal distribution and the standard deviation of the distribution is 5,000 miles. Crosset Truck Company bought 48 tires and found that the mean mileage for its trucks is 59,500 miles. Is Crosset’s experience different from that claimed by the manufacturer at the .05 significance level?