Question

A manufacturer of MP3 players conducts a set of comprehensive tests on the electrical functions of its product. All MP3 players must pass all tests prior to being sold. Of a random sample of 500 MP3 players, 20 failed one or more tests. Find a 90% confidence interval for the proportion of MP3 players from the population that pass all tests.

Answer 1

One-Proportion Confidence Interval

We need to construct the 90% confidence interval for the population proportion. We have been provided with the following information: The sample size is N = 500, the number of favorable cases is X = 480 and the sample proportion is pˉ​=X/N​=480/500​=0.96, and the significance level is α=0.1 Critical Value Based on the information provided, the significance level is α=0.1, therefore the critical value for this Two-tailed test is Zc​=1.6449. This can be found by either using excel or the Z distribution table. Margin of Error The confidence interval: Therefore, based on the data provided, the 90% confidence interval for the population proportion is 0.9456<p<0.9744, which indicates that we are 90% confident that the true population proportion p is contained by the interval (0.9456,0.9744)