Homework Clinic
Mathematics Clinic => Statistics => Topic started by: EY67 on Feb 14, 2020
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A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration (FDA) before its introduction into the market. The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Let μ1 be the true mean weight of individuals before starting the diet and let μ2 be the true mean weight of individuals after 3 weeks on the diet.
Summary information is as follows: 
= 5, sd = 1.58.
Test to determine if the diet is effective at reducing weight. Use α = .10.
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To determine if the diet is effective at reducing weight, we test:
H0: μD = 0
Ha: μD > 0
The test statistic is t = 
= 
= 7.07.
The rejection region requires 
in the upper tail of the t distribution with 
The rejection region is t > 1.533.
Since the observed value of the test statistic falls in the rejection region (t = 7.07 > 1.533), H0 is rejected. There is sufficient evidence to indicate that the diet is effective at reducing weight when testing at α = .10.
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Thank you
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Thank you