Every year, Fortune Magazine lists the 100 best companies to work for, based on criteria such as pay, benefits, turnover rate, and diversity. In 2013, the top three were Google, SAS, and CHG Healthcare. Of the top 30, 11 experienced double-digit job growth (10% or more), 16, single-digit growth ( $1 \%$ to $10 \%), 2$ had no growth, and Google did not report. Of the bottom 30, only 5 experienced double-digit job growth, 16 had single-digit growth, and 9 had no growth or job loss. Disregarding Google, is job growth in the best of the best places to work differently from job growth at the bottom of that elite list?

c) State the hypotheses.

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?

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

A subtle form of racial discrimination in housing is "racial steering." Racial steering occurs when real estate agents show prospective buyers only homes in neighborhoods already dominated by that family's race. This violates the Fair Housing Act of 1968. According to an article in Chance magazine (Vol. 14, no. 2 [2001]), tenants at a large apartment complex recently filed a lawsuit alleging racial steering. The complex is divided into two parts: Section A and Section B. The plaintiffs claimed that white potential renters were steered to Section A, while African-Americans were steered to Section B. The table displays the data that were presented in court to show the locations of recently rented apartments. Do you think there is evidence of racial steering?

$$\begin{array}{|l|cc|c|}\hline &\text { New Renters } \\ \hline & \text { White } & \text { Black } & \text { Total } \\ \hline \text { Section A } & 87 & 8 & 95 \\ \text { Section B } & 83 & 34 & 117 \\ \hline \text { Total } & 170 & 42 & 212 \\ \hline\end{array}$$

Every year, Fortune Magazine lists the 100 best companies to work for, based on criteria such as pay, benefits, turnover rate, and diversity. In 2013, the top three were Google, SAS, and CHG Healthcare. Of the top 30, 11 experienced double-digit job growth (10% or more), 16, single-digit growth ( $1 \%$ to $10 \%), 2$ had no growth, and Google did not report. Of the bottom 30, only 5 experienced double-digit job growth, 16 had single-digit growth, and 9 had no growth or job loss. Disregarding Google, is job growth in the best of the best places to work differently from job growth at the bottom of that elite list?

b) Check the assumptions.

According to the Agency for Healthcare Research and Quality, there were $409,706$ hospital visits for asthma-related illnesses in a recent year. The age distribution was as follows.

$$\begin{array}{cr} \hline \text{Age Range} & \text{Number}\\ \hline \text{Less than 1 year} & 7,866\\ 1- 17& 103,040\\ 18 - 44 & 79,659\\ 45-64 & 121,728\\ 65 - 84 & 80,649\\ \text{85 and up} & 16,764\\ \hline \text{Total} & 409,706\\ \end{array}$$

$\textbf{a.}\hspace{10pt}$ What is the probability that an asthma patient is between $18$ and $44$ years old?

$\textbf{b.}\hspace{10pt}$ What is the probability that an asthma patient is $65$ or older?

$\textbf{c.}\hspace{10pt}$ Using a cutoff of $0.05$, is it unusual for an asthma patient to be less than $1$ year old?

At a major credit card bank, the percentages of people who historically apply for the Silver, Gold, and Platinum cards are $60 \%, 30 \%$, and $10 \%$, respectively. In a recent sample of customers responding to a promotion, of 200 customers, 110 applied for Silver, 55 for Gold, and 35 for Platinum. Is there proof to indicate that the percentages for this promotion may be different from the historical proportions?

e) Using the critical value, what do you conclude about the null hypothesis at $\alpha=0.05$?

At a major credit card bank, the percentages of people who historically apply for the Silver, Gold, and Platinum cards are $60 \%, 30 \%$, and $10 \%$, respectively. In a recent sample of customers responding to a promotion, of 200 customers, 110 applied for Silver, 55 for Gold, and 35 for Platinum. Is there proof to indicate that the percentages for this promotion may be different from the historical proportions?

d) Find the $\alpha=0.05$ critical value for the $\chi^2$ distribution with the appropriate number of $\mathrm{df}$.

At a major credit card bank, the percentages of people who historically apply for the Silver, Gold, and Platinum cards are $60 \%, 30 \%$, and $10 \%$, respectively. In a recent sample of customers responding to a promotion, of 200 customers, 110 applied for Silver, 55 for Gold, and 35 for Platinum. Is there proof to indicate that the percentages for this promotion may be different from the historical proportions?

c) What does that say about the null hypothesis?

Does the statistic you calculated in the earlier exercise seem large in comparison to this mean? Describe briefly.

At a major credit card bank, the percentages of people who historically apply for the Silver, Gold, and Platinum cards are $60 \%, 30 \%$, and $10 \%$, respectively. In a recent sample of customers responding to a promotion, of 200 customers, 110 applied for Silver, 55 for Gold, and 35 for Platinum. Is there proof to indicate that the percentages for this promotion may be different from the historical proportions?

a) If the customers apply for the three cards according to the historical proportions, about how big, on average, would you expect the $\chi^2$ statistic to be (what is the mean of the $\chi^2$ distribution)?

Many factors affect the price of wine, including such qualitative characteristics as the variety of grape, location of the winery, and label. Researchers developed a regression model considering two quantitative variables: the tasting score of the wine and the age of the wine (in years) when released to the market. They found the following regression equation, with an $R^2$ of $65 \%$, to predict the price (in dollars) of a bottle of wine. Price $=6.25+1.22$ Tasting Score $+0.55 \mathrm{Age}$

One of these interpretations is accurate. Which is it? Describe what is wrong with the others.

a) The minimum price for a bottle of wine that has not aged is $\$ 6.25$.

Use the survey results in the table below to analyze differences in employee job satisfaction among organizations in the United States with different management styles.

e) Analyze the meaning of the results and state a conclusion.

Jake is installing a staircase so his children can have access to a tree house he built. The rise of the stairs is 7 inches and the run of each stair Is 10 Inches. What is the slope of the staircase, expressed as a fraction?

Use the survey results in the table below to analyze differences in employee job satisfaction among organizations in the United States with different management styles.

d) Test a suitable hypothesis and state your results.