Construct a 90% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers
A contributor for the local newspaper is writing an article for the weekly fitness section. To prepare for the story, she conducts a study to compare the exercise habits of people who exercise in the morning to the exercise habits of people who work out in the afternoon or evening. She selects three different health centers from which to draw her samples. The 56 people she sampled who work out in the morning have a mean of 5.5 hours of exercise each week. The 53 people surveyed who exercise in the afternoon or evening have a mean of 3.8 hours of exercise each week. Assume that the weekly exercise times have a population standard deviation of 0.7 hours for people who exercise in the morning and 0.3 hours for people who exercise in the afternoon or evening. Let Population 1 be people who exercise in the morning and Population 2 be people who exercise in the afternoon or evening.
Step 1 of 2 : Construct a 90% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers. Round the endpoints of the interval to one decimal place, if necessary.
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