Assignment:
Q1 A simple random sample of n = 300 full-time employees is selected from a company list containing the names of all, N = 5,000 full-time employees in order to evaluate job satisfaction.
a. Give an example of possible coverage error.
b. Give an example of possible nonresponse error.
c. Give an example of possible sampling error.
d. Give an example of possible measurement error.
Q2 Given a normal distribution with m = 100 and s = 10, if you select a sample of n = 25, what is the probability that X is.
a. less than 95?
b. between 95 and 97.5?
c. above 102.2?
d. There is a 65% chance that X is above what value?
Q3 Time spent using e-mail per session is normally distributed, with m = 8, minutes and s = 2 minutes, if you select a random sample of 25 sessions,
a. What is the probability that the sample mean is between 7.8 and 8.2 minutes?
b. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 7.8 and 8.2 minutes?
Q4 Assuming that the population is normally distributed, construct a 95% confidence interval estimate for the population mean for each of the following samples:
Sample A: 1, 1, 1, 1, 8, 8, 8, 8
Sample B: 1, 2, 3, 4, 5, 6, 7, 8
Explain why these two samples produce different confidence intervals even though they have the same mean and range.
Q5 A stationery store wants to estimate the mean retail value of greeting cards that it has in its inventory. A random
sample of 100 greeting cards indicates a mean value of $2.55 and a standard deviation of $0.44.
a. Assuming a normal distribution, construct a 95% confidence interval estimate of the mean value of all greeting cards in the store's inventory.
b. Suppose there were 2,500 greeting cards in the store's inventory. How are the results in (a) useful in assisting the store owner to estimate the total value of her inventory?
Q6 The start of the twenty-first century saw many corporate scandals and many individuals lost faith in business. In a 2007 poll conducted by the New York City-based Edelman Public Relations firm, 57% of respondents say they trust business to "do what is right." This percentage was the highest in the annual survey since 2001
a. Construct a 95% confidence interval estimate of the population proportion of individuals who trust business to "do what is right" assuming that the poll surveyed:
1. 100 individuals.
2. 200 individuals.
3. 300 individuals.
b. Discuss the effect that sample size has on the width of confidence intervals.