Question

Randomly selected statistics students of the author participated in an experiment to test their ability to determine when 60 seconds has passed. Forty students yielded a sample mean of

57.3 sec. Assume that the population standard deviation is σ = 8.5 sec.

1. a) Find the critical value zα /2 for a 82% confidence interval

2. b) Construct a 82% confidence interval estimate of the population mean of all statistics students. Use the z-table method.

3. c) Use TI84/83 calculator method.

4. d) Write a conclusion.

Answer 1

(a) The critical value zα /2 for a 82% confidence interval is 1.34.

(b) The 82% confidence interval estimate of the population mean of all statistics students is:

= x ± z*(σ/√n)

= 57.3 ± 1.34*(8.5/√40)

= 55.498, 59.102

The 82% confidence interval estimate of the population mean of all statistics students is between 55.498 and 59.102.

(c) The 82% confidence interval estimate of the population mean of all statistics students is between 55.50 and 59.10.

(d) We are 82% confident that the true population mean of all statistics students is between 55.50 and 59.10.