The Cornell National Social Survey ${ }^8$ polls 1000 U.S. adults each year throughout that time. One question asked in each survey was "How much does your family spend weekly on eating out?" The table shows the results for 2008 and 2010. Was there a change?

	2008	2010	Total
< $50//Wk	662	691	1353
$51-100	185	179	364
$101-150	71	57	128
$151-200	40	25	65
> $200	35	20	55
Total	993	972	1965

d) A calculation gives$\chi^2=9.581, $\mathrm{P}$=0.0481$. What conclusion do you draw?

Consumer complaints are frequently reported to the Better Business Bureau. Industries with the most complaints to the Better Business Bureau are often banks, cable and satellite television companies, collection agencies, cellular phone providers, and new car dealerships. The results for a sample of 200 complaints are in the file BBB.

Show the frequency and percent frequency of complaints by industry.

Better Business Bureau. Historically, the industries with the most complaints to the Better Business Bureau have been banks, cable and satellite television companies, collection agencies, cellular phone providers, and new car dealerships. The results for a sample of 200 complaints are contained in the file $B B B$.

a. Construct a frequency distribution for the number of complaints by industry.

Better Business Bureau. Historically, the industries with the most complaints to the Better Business Bureau have been banks, cable and satellite television companies, collection agencies, cellular phone providers, and new car dealerships. The results for a sample of 200 complaints are contained in the file $B B B$.

b. Using $\alpha=.01$, conduct a hypothesis test to determine whether the probability of a complaint is the same for the five industries. What is your conclusion?

Consumer complaints are frequently reported to the Better Business Bureau. In 2011, the industries with the most complaints to the Better Business Bureau were banks; cable and satellite television companies; collection agencies; cellular phone providers; and new car dealerships (USA Today, April 16, 2012). The results for a sample of 200 complaints are contained in the file BBB. a. Show the frequency and percent frequency of complaints by industry.

Consumer complaints are frequently reported to the Better Business Bureau. Industries with the most complaints to the Better Business Bureau are often banks, cable and satellite television companies, collection agencies, cellular phone providers, and new car dealerships. The results for a sample of 200 complaints are in the file BBB.

Which industry had the highest number of complaints?

A sample of 12 homes sold last week in St. Paul, Minnesota, revealed the following information. Draw a scatter diagram. Can we conclude that, as the size of the home (reported below in thousands of square feet) increases, the selling price (reported in $thousands) also increases?

A company conducted a survey regarding its new electric car and estimates that the selling price p of the vehicle, in thousands of dollars, and the number x of cars that will sell, measured in thousands, are related by the equation $p x^2+12 p x=28,000$. Compute and interpret $d x / d p$ and $d p / d x$ when the selling price is $36,000.

Church Attendance by Age Group. Bara Research Group conducted a survey about church attendance. The survey respondents were asked about their church attendance and asked to indicate their age. Use the sample data to determine whether church attendance is independent of age. Using a $.05$ level of significance, what is the $p$-value and what is your conclusion? What conclusion can you draw about church attendance as individuals grow older?

$$\begin{array}{cccc} 20 \text { to } 29 & 30 \text { to } 39 & 40 \text { to } 49 & 50 \text { to } 59 \\ 31 & 63 & 94 & 72 \\ 69 & 87 & 106 & 78 \end{array}$$

For each of several randomly selected years, the total number of points scored in the Super Bowl football game and the total number of new cars sold in the United States are recorded. For this sample of paired data, what does $r$ represent? What does $\rho$ represent? Without doing any research or calculations, estimate the value of $r$.

According to the U.S. Census Bureau's Current Population Survey, the mean and median 2012 income of people atleast 25 years old who had a bachelor's degree but no higher degree were $50,281 and$62,597. 13 Which of these numbers is the mean and which is the median? Explain your reasoning.

Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations.

$$\begin{array}{cl} & H_0: \mu_1-\mu_2=0 \\ H_A: \mu_1-\mu_2 \neq 0 \\ \bar{x}_1=57 & \bar{x}_2=63 \\ \sigma_1=11.5 & \sigma_2=15.2 \\ n_1=20 & n_2=20 \end{array}$$

a. Using the $p$-value approach, test whether the population means differ at the 5% significance level.

b. Repeat the hypothesis test using the critical value approach.

Test the following hypotheses by using the $\chi ^ { 2 }$ goodness of fit test. $H _ { 0 } : p _ { \mathrm { A } } = .40 , p _ { \mathrm { B } } = .40 ,$ and $p _ { \mathrm { C } } = .20$ $H _ { \mathrm { a } } :$ The population proportions are not $p _ { \mathrm { A } } = .40 , p _ { \mathrm { B } } = .40 ,$ and $p _ { \mathrm { C } } = .20$.

A sample of size 200 yielded 60 in category $A , 120$ in category $B ,$ and 20 in category $C$ . Use $\alpha = .01$ and test to see whether the proportions are as stated in $H _ { 0 }$ . a. Use the $p$ -value approach. b. Repeat the test using the critical value approach.

An engineer wanted to determine how the weight of a car affects gas mileage. The following data represent the weights of various domestic cars and their gas mileages in the city for the 2015 model year.

$$\begin{matrix} \text{Car} & \text{Weight (lb)} & \text{Miles per Gallon}\\ \text{Buick LaCrosse} & \text{4724} & \text{17}\\ \text{Cadillac XTS} & \text{4006} & \text{18}\\ \text{Chevrolet Cruze} & \text{3097} & \text{22}\\ \text{Chevrolet Impala} & \text{3555} & \text{19}\\ \text{Chrysler 300} & \text{4029} & \text{19}\\ \text{Dodge Charger} & \text{3934} & \text{19}\\ \text{Dodge Dart} & \text{3242} & \text{24}\\ \text{Ford FOcus} & \text{2960} & \text{26}\\ \text{Ford Mustang} & \text{3530} & \text{19}\\ \text{Lincoln MKZ} & \text{3823} & \text{18}\\ \end{matrix}$$

Determine which variable is the likely explanatory variable and which is the likely response variable.