Standard Error, Population Proportion, Random Samples, Etc.

1) Suppose N=70,000, n=17,500, and s=50
A. Compute the standard error of x using the finite population correction factor
B. Repeat Part A assuming n=35,000
C. Repeat part A assuming n=70,000
D. Compare parts A, B, C, and describe what happens to the standard error of x as n is increased.

2) Suppose you want to estimate a population proportion, p,p^=0.35,N=5,900, and n=1,900. Find an approximate 95% confidence interval for p.

3) A random sample of size n=20 was drawn from a population of size N=220. The measurements shown below were obtained.
40 28 43 22
33 27 47 21
55 40 27 35
18 39 39 36
48 49 53 53
A. Estimate u with an approximate 95% confidence interval.
B. Estimate p, the proportion of measurements in the population that are greater than 30, with an approximate 95% confidence interval.

4) The random sample shown below was selected from a normal distribution. 8,6,3,6,10,3

A. Construct a 99% confidence interval for the population mean u.
B. Assume that sample mean x and sample standard deviation s remain exactly the same as those you just calculated but that are based on a sample of n=25 observations. Repeat part A. What is the effect of increasing the sample size on the width of the confidence intervals?

5) In order to evaluate the reasonableness of a firm's stated total value of its parts inventory, an auditor randomly samples 50 of the total 600 parts in stock, prices each part, and reports the results shown in the table. Use this information to answer the following questions:
Part Price $106 $65 $63 $57 $56 $105 $70 $19
Sample Size 7 4 7 4 8 10 4 6

A. Give a point estimate of the mean value of the parts inventory.
B. Find the estimated standard error of the point estimate of part A.
C. Find the limits of a 95% confidence interval for the mean.
D. The firm reported a means part inventory value of $55. What does the confidence interval of part c suggest about the reasonableness of the firm's reported figure?