Question

A researcher was interested in comparing the amount of time spent watching television by women and by men. Independent simple random samples of 14 women and 17 men were selected, and each person was asked how many hours he or she had watched television during the previous week. The following 99% confidence interval was obtained for µ1 - µ2 the difference between the mean amount of time spent watching television for women and the mean amount of time spent watching television for men: -5.73 hrs. < µ1 - µ2 < 4.13 hrs. What does the confidence interval suggest about the population means?

Answer 1

Here, alpha=0.10.

Lower bound = -5.73

Upper bound = 4.13

The confidence interval suggests that there is 99% chance that the confidence interval we calculated which is between -5.73 and 4.13, contains the true population mean.

The population mean has one value. If we repeated experiment, that value wouldn't change. Therefore, it isn't strictly correct to ask about the probability that the population mean lies within a certain range.