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.
a) Find the critical value zα /2 for a 82% confidence interval
b) Construct a 82% confidence interval estimate of the population mean of all statistics students. Use the z-table method.
c) Use TI84/83 calculator method.
d) Write a conclusion.
(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.
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