A powder diet is tested on 49 people, and a liquid diet is tested on 36 differen

Question

A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a standard deviation of 14 pounds. Conduct a hypothesis test at the 5% level.

State the distribution to use for the test. (Enter your answer in the form z or tdf where df is the degrees of freedom. Round your answer to two decimal places.)

Explanation / Answer

Use a 2 sample t-test with independent samples and df = n1 + n2 -2 = 49 + 36 - 2 = 83

H0: mp -ml = 0

H1: mp -ml < 0, Liquid Diet yields higher mean weight loss.

tstat = (x1-bar - x2-bar) /sp(sqrt(1/n1 + 1/n2) where sp is pooled variance given by

sp = sqrt( ((n1-1)s12 + (n2-1)s22 )/df )

     = sqrt(48*122 + 35*142/83) = 12.8813

tstat = (42 - 45)/12.88 (1/49 + 1/36)

      = -3/.621 = -4.83

Critical t-value for a lower one-tail test with 83 df is -1.66.

Decision rule is reject NULL if tstat < tcrit and since -4.83 < -1.66, reject H0 and conclude that liquid diet yields a higher mean loss than a power diet.

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