A couple will retire in 50 years; they plan to spend about $30,000 a year in retirement, which should last about 25 years. They believe that they can earn 8% interest on retirement savings.

a. If they make annual payments into a savings plan, how much will they need to save each year? Assume the first payment comes in 1 year. b. How would the answer to part (a) change if the couple also realize that in 20 years they will need to spend$60,000 on their child’s college education?

The following are selected transactions of the specific-purpose fund, the plant fund, and the endowment fund of Toddville Hospital, a not-for-profit entity:

1. Received in the endowment fund new permanent endowments totaling $150,000 and new term endowments totaling$120,000.

2. Received in the plant replacement and expansion fund pledges of $1,500,000 for the new wing and estimated uncollectibles at 10 percent.

3. Received in the specific-purpose fund gifts of$50,000 for research and $30,000 for education.

4. Received the following interest and dividends on investments:

$$\begin{array}{lr} \text{Endowment fund (permanent)} & \$100,000 \\ \text{Plant fund} & 45,000 \\ \text{Specific-purpose fund (research)} & 31,000 \\ \end{array}$$

This year's interest and dividends in the endowment fund have a donor-imposed permanent restriction.

5. Notified that the specific-purpose fund in the general fund had fulfilled the agreements related to restricted gifts as follows:

$$\begin{array}{lr} \text{Research} & \$55,000 \\ \text{Education} & 32,000\\ \end{array}$$

Transferred cash of $70,000 to the general fund with the balance to be sent later.

6. Made the following investments:

$$\begin{array}{lr} \text{Endowment fund} & \$270,000 \\ \text{Plant fund} & 160,000 \\ \text{Specific-purpose fund} & 75,000 \\ \end{array}$$

Required

Prepare appropriate journal entries for the transactions in the specific-purpose fund, plant fund, and endowment fund.

A survey firm wants to ask a random sample of adults in Ohio if they support an increase in the state sales tax from 5.75% to 6%, with the additional revenue going to education. Let $\hat{p}$ denote the proportion in the sample who say that they support the increase. Suppose that 40% of all adults in Ohio support the increase. If the survey firm wants the standard deviation of the sampling distribution of $\hat{p}$ to equal 0.01, how large a sample size is needed? (a) 1500 (b) 2400 (c) 2401 (d) 2500 (e) 9220

What is normal, when it comes to people's body temperatures? A random sample of 130 human body temperatures, provided by Allen Shoemaker in the Journal of Statistical Education, had a mean of 98.25$^{\circ}$ and a standard deviation of 0.73$^{\circ}$. a. Construct a 99% confidence interval for the average body temperature of healthy people. b. Does the confidence interval constructed in part a contain the value 98.6$^{\circ}$, the usual average temperature cited by physicians and others? If not, what conclusions can you draw?

Which of the following is a capital letter, and which is not? Explain your responses. a. A video poker game machine at a local bar that takes quarters b. A $\$ 10$ bill c. A college education d. The Golden Gate Bridge e. The shirts on the rack at Sears f. A government bond g. The Empire State Building h. A savings account i. The Washington Monument j. A Honda plant in Marysville, Ohio

Suppose a metropolitan area is divided into four school districts: 1, 2, 3, 4. The State Board of Education keeps track of the number of student transfers from one district to another and the student transfers within a district. This information is recorded each year in a ${4} \times {4}$ table as shown here. The entry in row 1, column 3 (314), for example, shows the number of student transfers from district 1 to district 3 for the year. The entry in row 1, column 1 (243) shows the number of student transfers within district 1.

$$\begin{array}{l|lll} {} & {1} & {2} & {3} & {4} \\ \hline 1 & {243} & {187} & {314} & {244} \\ {2} & {215} & {420} & {345} & {172} \\ {3} & {197} & {352} & {385} & {261} \\ {4} & {340} & {135} & {217} & {344}\end{array}$$

Suppose there are n school districts, and the Board of Education maintains an ${n} \times {n}$ table. a. Write a pseudocode algorithm to print out the table, that is, to print each of the entries in the table. Write an expression for the number of print statements the algorithm executes. b. Write a pseudocode algorithm to print n copies of the table, one to give to each of the n school district supervisors. Write an expression for the number of print statements the algorithm executes. c. What is the order of magnitude of the work done by the algorithm in Part b if the unit of work is printing a table element?

Education A professor assigns $6$ homework projects and then, during the next class, rolls a die to determine which one of the $6$ projects to grade. If a student has completed $2$ of the assignments, what is the probability that the professor will grade a project that the student has completed?

Here are more proposed survey questions for the survey in the given exercise :

Question 3: Do you find that the slow speed of DSL Internet access reduces your enjoyment of web services? Question 4: Given the growing importance of high-speed Internet access for your children's education, would you subscribe to such a service if it were offered?

b) Propose a question with better wording.

At a large factory, the employees were surveyed and classified according to their level of education and whether they attend a sports event at least once a month. The data are shown in the table.

If an employee is chosen at random, find the probability that

a. The employee attends sports events regularly, given that he or she graduated from college (2- or 4year degree)

b. Given that the employee is a high school graduate, he or she does not attend sports events regularly

Imagine that someone offered you a choice: You could spend four years studying at the world's best university, but you would have to keep your attendance there a secret. Or you could be awarded an official degree from the world's best university, but you couldn't actually attend. Which choice do you think would enhance your future earnings more? What does your answer say about the debate over signaling versus human capital in the role of education?

A national opinion poll recently estimated that 44%($\hat{p}$=0.44) of all adults agree that parents of school-age children should be given vouchers good for education at any public or private school of their choice. The polling organization used a probability sampling method for which the sample proportion $\hat{p}$ has a normal distribution with standard deviation about 0.015. If a sample were drawn by the same method from the state of New Jersey (population 7.8 million) instead of from the entire United States (population 280 million), would this standard deviation be larger, about the same, or smaller? Explain your answer.

Upon the birth of your son, you open an account to fund his college education. You deposit $1,500 to open the account. Each year, on his birthday, you make another deposit, each being 15 percent larger than the previous deposit. The last deposit is on his seventeenth birthday. The account has earnings of 6 percent per year compounded annually. How much money is in the account on his eighteenth birthday, one year after the last of eighteen deposits?

Work each investment problem using simple interest. Arlene Frank is saving money for her college education. She deposited some money in a savings account paying 5% and $1200 less than that amount in a second account paying 4%. The two accounts produced a total of$141 interest in 1 yr. How much did she invest at each rate?

The amounts A (in billions of dollars) donated to support higher education in the United States from 2000 through 2007 are shown in the table, where represents the year, with t=0 corresponding to 2000.

$$\begin{array}{|c|c|} \hline \text { Year, } t & \text { Amount, } A \\ \hline 0 & 23.2 \\ 1 & 24.2 \\ 2 & 23.9 \\ 3 & 23.9 \\ 4 & 24.4 \\ 5 & 25.6 \\ 6 & 28.0 \\ 7 & 29.8 \\ \hline \end{array}$$

Use a graphing utility to create a scatter plot of the data.