A company claims that its 12 week special exercise program significantly reduces

Question

A company claims that its 12 week special exercise program significantly reduces weight. A random sample of 6 persons was selected, and these persons were put on this exercise program for 12 weeks. The following table gives the before and after weights.

a. Make a 95% confidence interval for the mean difference d of the paired population differences (weight before – weight after).

b. Using 1% significance level, can you conclude that the mean weight loss for all persons due to this special exercise program is greater than zero?

Explanation / Answer

a) From information given, mean difference, dbar=9.83, standard deviation of difference, sd=7.19, n=6 pairs, Compute standard error of dbar.

SE(dbar)=sd/sqrt n=7.19/sqrt 6=2.94

95% c.i=dbar+-tcritical SE(dbar), t critical corresponds to t score at alpha=0.05, and df=n-1=5

=9.83+-2.571*2.94

=2.28 to 17.38

b) t test statistic=(dbar-0)/SE(dbar)

=(9.83-0)/2.94

=3.35

p value at df=5, 0.020.

p value is not less than alpha=0.01. Fail to reject null hypothesis. There is not sufficient sample evidence to conclude that mean weigh loss for all patients due to this special exercise program is greater than 0.

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