Question: 401(k) Participation rates. Named for the section of the 1978 Internal Revenue Code that authorized them, 401(k) plans permit employees to shift part of their before-tax salaries into investments such as mutual funds. Employers typically match 50% of the employee's contribution up to about 6% of salary. One company, concerned with what it believed was a low employee participation rate in its 401(k) plan, sampled 30 other companies with similar plans and asked for their 401(k) participation rates. The following rates (in percentages) were obtained and are saved in the RATE401K file.

80 76 81 77 82 80 85 60 80 79 82 70

88 85 80 79 83 75 87 78 80 84 72 75

90 84 82 77 75 86

1. Construct a 90% confidence interval for the mean participation rate for all companies that have 401(k) plans.
2. Interpret the interval in the context of this problem.
3. What assumption is necessary to ensure the validity of this confidence interval?
4. If the company that conducted the sample has a 71% participation rate, can it safely conclude that its rate is below the population mean rate for all companies with 401(k) plans? Explain.
5. If in the data set the 60% had been 80%, how would the center and width of the confidence interval you constructed in part a be affected?

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