Question

. You are performing research into the current physiological measurements of men and women. At your request, a medical research center sends you the weights, in pounds, of a group of sixteen randomly selected male patients and an independent group of sixteen randomly selected female patients. The mean weight of the men in the sample was 192 pounds with a standard deviation of 26.746 pounds. The mean weight of the women in the sample was 159 pounds with a standard deviation of 13.272 pounds. Determine whether there is a statistically significant difference in the weights between men and women. Use an alpha of 5%. If there is a statistically significant difference between the two groups, find the 99% confidence interval for the difference in weights.

Answer 1

The test hypothesis is

This is a two-sided test because the alternative hypothesis is formulated to detect differences from the hypothesized difference in mean values on either side.

Now, the value of test static can be found out by following formula:

Degrees of freedom on the t-test statistic are n1 + n2 - 2 = 16 + 16 - 2 = 30

Since t0 = 4.4209 > 2.0422724563012373 = t{0.025, 30}, we reject the null hypothesis

Yes, there is a statistically significant difference in the weights between men and women.

Confidence interval(in %) = 99

Since we know that

Required confidence interval = (33.0-20.5273, 33.0+20.5273)

Required confidence interval = (12.47, 53.53)

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