Question

Many people take ginkgo supplements advertised to improve memory. Are these over-the-counter supplements effective? In a study reported in the paper “Ginkgo for memory Enhancement” (Journal of the American Medical Association), elderly adults were assigned at random to either a treatment or a control group. The 104 participants who were assigned to the treatment group took 40 mg of ginkgo three times a day for six weeks. The 115 participants assigned to the control group took a placebo pill three times a day for six weeks. At the end of six weeks, the Wechsler Memory Scale (a test of short-term memory) was administered. Higher scores indicate better memory function. Summary values are given in the following table.

Based on these results, we want to find whether there is evidence that taking 40 mg of ginkgo three times a day is effective in increasing mean performance on the Wechsler Memory Scale.

Calculate the test statistic for the test above. (round test statistic to 2 decimal places)

What is the cutoff value for the rejection region? Use significance level 0.05. (round to 2 decimal places)

What's your decision on the hypothesis test above? Use significance level 0.05.
(type Reject for Reject Ho, type FTR for Fail to Reject Ho)

Answer 1

Assume that μ₁ is mean score for the given ginkgo, μ₂ is mean score for the given placebo.

Our hypothesis is,

H₀: μ₁-μ₂=0 i.e mean score of ginkgo doze is same as mean score of placebo doze.

vs

H₁: μ₁-μ₂>0 i.e mean score of ginkgo doze is greater than mean score of placebo doze.

Here, significant level is 0.05