Assignment:
1. The manager of a convenience store has taken a random sample of 64 customers. The average length of time it took these 64 customers to check out was 3.5 minutes. It is known that the population standard deviation of checkout times is 1.5 minute.
a. Calculate standard error of the mean.
b. Calculate the margin of error at a 95% confidence level.
c. Calculate the confidence interval at a 95% confidence level.
d. What sample size would the convenience store manager need to reduce the margin of error to .25 minutes?
2. The admissions director at a local university claims the average age of the students attending her university is at least 24 years old. Her assistant believes the students are younger than that, so she surveys a random sample of 16 students and finds their average age to be 25 years. Assume the sample distribution is normal and has a population standard deviation of 2 years.
a. What is the alternative and null hypotheses?
b. What is the test statistic?
c. What is the p-value?
d. What is your conclusion about the stated hypotheses at a 95% confidence level?
3. A random sample of 25 GRE scores of students applying for merit scholarships showed an average of 1200 with a sample standard deviation of 240.
a. Calculate standard error of the mean.
b. Calculate the margin of error at an 80% confidence level.
c. Calculate the confidence interval at an 80% confidence level.
4. The Economic Policy Institute periodically issues reports on wages of entry-level workers. The institute reported that entry-level wages for male college graduates were $21.68 per hour and for female college graduates were 18.80 per hour in 2011. Assume the population standard deviation for male graduates is $2.30 and for female graduates it is $2.05. (Review Chapter 7 for this problem)
a. What is the probability that a sample of 50 male graduates will provide a sample mean within $.50 of the population mean, $21.68?
b. What is the probability that a sample of 50 female graduates will provide a sample mean within $.50 of the population mean, $18.80?
c. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $.50 of the population mean? Why?
d. What is the probability that a sample of 120 female graduates will provide a sample mean more than $.30 below the population mean?
5. What is the value of +z?/2 for a 97% confidence level?
6. CCN and ActMedia provided a television channel targeted to individuals waiting in supermarket checkout lines. The channel showed news, short features, and advertisements. The length of the program was based on the assumption that the population mean time a shopper stands in a supermarket checkout line is 8 minutes. A sample of actual waiting times will be used to test this assumption and determine whether actual mean waiting times differs from this assumption.
a. Formulate the hypotheses for this application.
b. A sample of 120 shoppers showed a sample mean waiting time of 8.4 minutes. Assume a population standard deviation of 3.2 minutes. What is the p-value (round calculations to third decimal place)?
c. At alpha = .05, what is your conclusion?
d. Compute a 95% confidence interval for the population mean (round calculations to third decimal place). Does it support your conclusion in "c"?