Question

A.) What price do farmers get for their watermelon crops? In the third week of July, a random sample of 42 farming regions gave a sample mean of x = $6.88 per 100 pounds of watermelon. Assume that ? is known to be $1.98 per 100 pounds.

Find the sample size necessary for a 90% confidence level with maximal error of estimate E = 0.45 for the mean price per 100 pounds of watermelon. (Round up to the nearest whole number.)

_ farming regions

B.) Jobs and productivity! How do retail stores rate? One way to answer this question is to examine annual profits per employee. The following data give annual profits per employee (in units of 1 thousand dollars per employee) for companies in retail sales. Assume ? ? 3.7 thousand dollars.

3.6	6.8	3.7	8.4	8.5	5.4	8.3	6.1	2.6	2.9	8.1	?1.9
11.9	8.2	6.4	4.7	5.5	4.8	3.0	4.3	?6.0	1.5	2.9	4.8
?1.7	9.4	5.5	5.8	4.7	6.2	15.0	4.1	3.7	5.1	4.2

Use a calculator or appropriate computer software to find x for the preceding data. (Round your answer to two decimal places.)
_ thousand dollars per employee

Let us say that the preceding data are representative of the entire sector of retail sales companies. Find an 80% confidence interval for ?, the average annual profit per employee for retail sales. (Round your answers to two decimal places.)

lower limit _ thousand dollars

upper limit _ thousand dollars

Find an 95% confidence interval for ?, the average annual profit per employee for retail sales. (Round your answers to two decimal places.)

lower limit _ thousand dollars

upper limit _ thousand dollars

Answer 1

a) At 90% confidence interval the critical value is z_0.05 = 1.645

E = 0.45

or, z_0.05 * = 0.45

or, 1.645 * 1.98/ = 0.45

or, n = (1.645 * 1.98/0.45)^2

or, n = 53

B) = 5.04

At 80% confidence interval the critical value is z_0.1 = 1.28

The 80% confidence interval is

+/- z_0.1 *

= 5.04 +/- 1.28 * 3.7/

= 5.04 +/- 0.80

= 4.24, 5.84

At 95% confidence interval the critical value is z_0.025 = 1.96

The 95% confidence interval is

+/- z_0.025 *

= 5.04 +/- 1.96 * 3.7/

= 5.04 +/- 1.23

= 3.81, 6.27