Question

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Assume that the samples are independent, simple random samples, and either both sample sizes are at least 30 or both populations are approximately normal. 1. 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 work out 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 49 people she sampled who worked out in the morning have a mean of 4.1 hours of exercise each week. The 54 people surveyed who exercise in the afternoon or evening have a mean of 3.7 hours of exercise each week. Construct and interpret a 95% 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. Assume that the weekly exercise times have a population standard deviation of 0.7 hours for people who exercise in the morning and 0.5 hours for people who exercise in the afternoon or evening.

Answer 1

We will calculate the 95% confidence interval by using the value of z statistics.

Let ni and no be the population samble Size Let w and no be the sample size and first and second pobulation (l.e. first population is morning Poopulation and second loopulation is evening population) .. ni -49, ng - 54. let u and & be the mean and sto deviation of first loopulation and and I be the mean and sodo of second polulation u = 4.1 , Ś = 0x7 M = 3. l so = 0.5 So, the 95. 1. confidence interval for true dift - elence in population is given by (n-Me) & 1.96 S.E. (an-T ) where 1.96 is the tabulated Ole critical alue of a at 5% level of signiticance. (14- 22 1096 S•&• (-ke) = (4.1 – 3. 7) +1-96, (0.7)&#6065je ro. Sof(4-22)7 vya si = 1 S² + S 0:4 I 196 0.01 to 01462.96 un na = I 0.4+ 1.96 Xould out 0.2352 - 0.4-0.2352, 0.4 +0.2352 0.1648, 0.6352 (0-1648 , 0-6352) -