Calculating the Sample Size n: Continuous and Binary Random Variables · Exercise 47

Suppose that an accounting firm does a study to determine the time needed to complete one person’s tax forms. It randomly surveys 100 people. The sample mean is 23.6 hours. There is a known standard deviation of 7.0 hours. The population distribution is assumed to be normal.

(a) (a) $\stackrel{-}{x}$ =________
(b) σ =________
(c) n =________
(b) In words, define the random variables X and $\bar{X}$.
(c) Which distribution should you use for this problem? Explain your choice.
(d) Construct a 90% confidence interval for the population mean time to complete the tax forms.
(a) State the confidence interval.
(b) Sketch the graph.
(e) If the firm wished to increase its level of confidence and keep the error bound the same by taking another survey, what changes should it make?
(f) If the firm did another survey, kept the error bound the same, and only surveyed 49 people, what would happen to the level of confidence? Why?
(g) Suppose that the firm decided that it needed to be at least 96% confident of the population mean length of time to within one hour. How would the number of people the firm surveys change? Why?

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Business Statistics 2e · §8.4 Calculating the Sample Size n: Continuous and Binary Random Variables · Exercise 47