Question

A.) For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

How hard is it to reach a businessperson by phone? Let p be the proportion of calls to businesspeople for which the caller reaches the person being called on the first try.

(a) If you have no preliminary estimate for p, how many business phone calls should you include in a random sample to be 80% sure that the point estimate p? will be within a distance of 0.04 from p? (Round your answer up to the nearest whole number.)
phone calls

(b) A report states that businesspeople can be reached by a single phone call approximately 14% of the time. Using this (national) estimate for p, answer part (a). (Round your answer up to the nearest whole number.)
phone calls

B.) Do you want to own your own candy store? Wow! With some interest in running your own business and a decent credit rating, you can probably get a bank loan on startup costs for franchises such as Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain Chocolate Factory. Startup costs (in thousands of dollars) for a random sample of candy stores are given below. Assume that the population of x values has an approximately normal distribution.

98

177

132

95

75

94

116

100

85

(a) Use a calculator with mean and sample standard deviation keys to find the sample mean startup cost x and sample standard deviation s. (Round your answers to one decimal place.)

x =	thousand dollars
s =	thousand dollars

(b) Find a 90% confidence interval for the population average startup costs ? for candy store franchises. (Round your answers to one decimal place.)

lower limit	thousand dollars
upper limit	thousand dollars

C.) Let x be a random variable representing dividend yield of bank stocks. We may assume that x has a normal distribution with ? = 2.0%. A random sample of 10 bank stocks gave the following yields (in percents).

5.7

4.8

6.0

4.9

4.0

3.4

6.5

7.1

5.3

6.1

The sample mean is x = 5.38%. Suppose that for the entire stock market, the mean dividend yield is ? = 4.4%. Do these data indicate that the dividend yield of all bank stocks is higher than 4.4%? Use ? = 0.01.
(a) What is the level of significance?

Compute the z value of the sample test statistic. (Round your answer to two decimal places.)


(b) Find (or estimate) the P-value. (Round your answer to four decimal places.)

Answer 1

A)

Since no estimate of popualiton poportion is given so let

The critical value of z for 80% confidence interval, using excel function "=NORMSINV(0.9)", is .

The margin of error E= 0.04, so required sample size will be

So required sample size for 80% confidence interval is 256.

(b)

Here we have

The critical value of z for 80% confidence interval using excel function "=NORMSINV(0.9)" is .

The margin of error E= 0.04, so required sample size will be

So required sample size for 80% confidence interval is 124.