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?

d) Test a suitable hypothesis and state your results.

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.

Census data for New York City indicate that 29.2% of the under-18 population is white, 28.2% black, 31.5% Latino, 9.1% Asian, and 2% other ethnicities. The New York Civil Liberties Union points out that, of 26,181 police officers, 64.8% are white, 14.5% black, 19.1% Hispanic, and 1.4% Asian. Do the police officers reflect the ethnic composition of the city's youth? Test an appropriate hypothesis and state your conclusion.

Census data for New York City indicate that 29.2% of the under-18 population is white, 28.2% black, 31.5% Latino, 9.1% Asian, and 2% other ethnicities. The New York Civil Liberties Union points out that, of 26,181 police officers, 64.8% are white, 14.5% black, 19.1% Hispanic, and 1.4% Asian. Do the police officers reflect the ethnic composition of the city’s youth? Test an appropriate hypothesis and state your conclusion.

A market researcher working for the bank in the earlier exercise wants to know if the distribution of applications by card is the same for the past three mailings. She takes a random sample of 200 from each mailing and counts the number applying for Silver, Gold, and Platinum. The data follow:

e) How many degrees of freedom does it have?

According to the Gallup Poll, $27\%$ of U.S. adults have high levels of cholesterol. Gallup reports that such elevated levels "could be financially devastating to the U.S. healthcare system" and are a major concern to health insurance providers. According to recent analyses, cholesterol levels in healthy U.S. adults average about $215 \mathrm{mg} / \mathrm{dL}$ with a standard deviation of about $30 \mathrm{mg} / \mathrm{dL}$ and are roughly Normally distributed. If the cholesterol levels of a sample of 42 healthy U.S. adults are taken, what is the probability that the mean cholesterol level of the sample:

c) Will be less than 200?

According to the Gallup Poll, $27\%$ of U.S. adults have high levels of cholesterol. Gallup reports that such elevated levels "could be financially devastating to the U.S. healthcare system" and are a major concern to health insurance providers. According to recent analyses, cholesterol levels in healthy U.S. adults average about $215 \mathrm{mg} / \mathrm{dL}$ with a standard deviation of about $30 \mathrm{mg} / \mathrm{dL}$ and are roughly Normally distributed. If the cholesterol levels of a sample of 42 healthy U.S. adults are taken,

d) If the sample size were increased to 100, how would your answers to parts a-c change?

An information technology (IT) consulting firm specializing in healthcare solutions wants to study communication deficiencies in the health care industry. A random sample of 70 health care clinicians reveals the following:

• Time wasted in a day due to outdated communication technologies: $\overline{X}$ = 45 minutes, S = 10 minutes.

• Thirty-six health care clinicians cite inefficiency of pagers as the reason for the wasted time.

a. Construct a 99% confidence interval estimate for the population mean time wasted in a day due to outdated communication technologies.

b. Construct a 95% confidence interval estimate for the population proportion of health care clinicians who cite inefficiency of pagers as the reason for the wasted time.

Gold is a face-centered cubic structure that has a unit cell edge length of $4.08 \text{\AA}$. There are four gold atoms per unit cell. How many gold atoms are there in a sphere that is $20 \mathrm{~nm}$ in diameter? Recall that the volume of a sphere is $\frac{4}{3} \pi t^3$.

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?

A chain that specializes in healthy and organic food would like to compare the sales performance of two of its primary stores in the state of Massachusetts. These stores are both in urban, residential areas with similar demographics. A comparison of the weekly sales randomly sampled over a period of nearly two years for these two stores yields the next information:

e) Would you expect a $99 \%$ confidence interval to be wider or narrower? Describe.

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