The Economic Policy Institute periodically issues reports on wages of entry level workers. The institute reported that entry level wages for male college graduates were $\$21.68$ per hour and for female college graduates were $\$18.80$ per hour in 2011 (Economic Policy Institute website, March 30, 2012). Assume the standard deviation for male graduates is $\$2.30$, and for female graduates it is $\$2.05$.

a. What is the probability that a sample of 50 male graduates will provide a sample mean within $\$.50$ of the population mean, $\$21.68$?

b. What is the probability that a sample of 50 female graduates will provide a sample mean within $\$.50$ of the population mean, $\$18.80$?

c. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $\$.50$ of the population mean? Why?

d. What is the probability that a sample of 120 female graduates will provide a sample mean more than $\$.30$ below the population mean?

The Economic Report of the President contains statistical information about the economy as well as the Council of Economic Advisers’ analysis of current policy issues. Find a recent copy of this annual report at your library and read a chapter about an issue that interests you. Summarize the economic problem at hand and describe the council’s recommended policy.

The College Board reported the following mean scores for the three parts of the Scholastic Aptitude Test (SAT) ($The ~World ~Almanac$, 2009):

$$\textrm{Critical Reading} ~~502$$

$$\textrm{Mathematics}~~~~~~~ 515$$

$$\textrm{Writing} ~~~~~~~~~~~~~~~494$$

Assume that the population standard deviation on each part of the test is $\sigma=100.$ a. What is the probability a random sample of $90$ test takers will provide a sample mean test score within $10$ points of the population mean of $502$ on the Critical Reading part of the test? b. What is the probability a random sample of $90$ test takers will provide a sample mean test score within $10$ points of the population mean of $515$ on the Mathematics part of the test? Compare this probability to the value computed in part (a). c. What is the probability a random sample of $100$ test takers will provide a sample mean test score within $10$ of the population mean of $494$ on the writing part of the test? Comment on the differences between this probability and the values computed in parts (a) and (b).

State Rainfalls. According to the Current Results website, the state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches. Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York have been taken.

a. Show the probability distribution of the sample mean annual rainfall for California.

The Economic Policy Institute periodically issues reports on wages of entry-level workers. The institute reported that entry-level wages for male college graduates were $21.68 per hour and for female college graduates were$18.80 per hour in 2011. Assume that the standard deviation for male graduates is $2.30 and for female graduates it is$2.05.

In which of the preceding two cases, part (a) or part (b), is the standard error of $\bar{x}$ smaller? Why?

The Economic Policy Institute periodically issues reports on the wages of entry-level workers. The institute reported that entry-level wages for male college graduates were $\$ 21.68$ per hour and for female college graduates were $\$ 18.80$ per hour in 2011 (. Suppose the standard deviation for male graduates is $\$ 2.30$, and for female graduates, it is $\$ 2.05$.

d. What is the possibility that a sample of 120 female graduates will provide a sample mean more than $\$ .30$ below the population mean?

The state of California has a mean annual rainfall of 22 inches, whereas the state of New York has a mean annual rainfall of 42 inches (Current Results website, October 27, 2012). Assume that the standard deviation for both states is 4 inches. A sample of 30 years of rainfall for California and a sample of 45 years of rainfall for New York has been taken.

a. Show the probability distribution of the sample mean annual rainfall for California.

b. What is the probability that the sample mean is within I inch of the population mean for California?

c. What is the probability that the sample mean is within 1 inch of the population mean for New York?

d. In which case, part (b) or part (c), is the probability of obtaining a sample mean within 1 inch of the population mean greater? Why?

A production process is checked periodically by a quality control inspector. The inspector selects simple random samples of $30$ finished products and computes the sample mean product weights $\bar{x}$. If test results over a long period of time show that $5\%$ of $\bar{x}$ the values are over $2.1$ pounds and $5\%$ are under $1.9$ pounds, what are the mean and the standard deviation for the population of products produced with this process?

A company manager asked $500$ of her employees if they would rather receive cash or an extra vacation day as a bonus. Use the information in the table to complete the problems below.

Bonus Preferences

a. What is the probability that an employee would rather receive a vacation day, given that the employee is female?

b. What is the probability that an employee would rather receive cash, given that the employee is male?

A simple random sample of 5 months of sales data provided the following information:

$$\textrm{Month:} ~~~~~~~~1~~~~~2~~~~3~~~~4~~~~5$$

$$\textrm{Units Sold:} ~~94 ~100~~ 85 ~~94 ~~92$$

Develop a point estimate of the population mean number of units sold per month.

The Economic Policy Institute periodically issues reports on wages of entry-level workers. The institute reported that entry-level wages for male college graduates were $21.68 per hour and for female college graduates were$18.80 per hour in 2011 (Economic Policy Institute website, March 30, 2012). Assume the standard deviation for male graduates is $2.30, and for female graduates it is$2.05.

a. What is the probability that a sample of 50 male graduates will provide a sample mean within $.50 of the population mean,$21.68?

b. What is the probability that a sample of 50 female graduates will provide a sample mean within $.50 of the population mean,$18.80?

c. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $.50 of the population mean? Why?

d. What is the probability that a sample of 120 female graduates will provide a sample mean more than$.30 below the population mean?

A market research firm conducts telephone surveys with a $40\%$ historical response rate. What is the probability that in a new sample of $400$ telephone numbers, at least $150$ individuals will cooperate and respond to the questions? In other words, what is the probability that the sample proportion will be at least $150/400 = .375$?

Promotion discrimination? The table indicates the rank attained by male and female officers in the New York City Police Department (NYPD). Do these data indicate that men and women are equitably represented at all levels of the department? (All possible ranks in the NYPD are shown.)

$$\begin{array}{lrc} & \text { Male } & \text { Female } \\ \text { Officer } & 21,900 & 4281 \\ \text { Detective } & 4058 & 806 \\ \text { Sergeant } & 3898 & 415 \\ \text { Lieutenant } & 1333 & 89 \\ \text { Captain } & 359 & 12 \\ \text { Higher Ranks } & 218 & 10\end{array}$$

e) State the hypotheses.

What is the probability that a sample of 50 female graduates will provide a sample mean within $.50 of the population mean,$18.80?