PROBLEM 5 A study was done on body temperatures of men and women. The results ar

Question

PROBLEM 5 A study was done on body temperatures of men and women. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do *not* assume that the population standard deviations are equal. Do not* assume that the population standard Compute a 95% confidence interval for the difference in the two population means (Ha-Ha). Men Women 14 97.66"F 0.79 H2 15 97.22 °F 0.65 °F SHOW YOUR WORK: Yes, even if you rely on technology to compute the confidence interval, you need to indicate the name of the procedure and the formular that applies.

Explanation / Answer

Here, we have to calculate 95% confidence interval. Here, populatin standard deviations are not equal.

Degree of freedom dF =  [s12 /n1 + s22 /n2] 2 / [(1/n1 -1) (s12 /n1)2 + (1/n2 -1) (s22 /n2)2 ]

dF = [0.792 /14 + 0.652 /15]2 / [ (1/13) * (0.792 /14)2 + 1/14 * (0.652 /15)2 ]

dF = 25.26 or 25 (in integer)

Confidence interval for sample mean difference 95% CI = (1 - 2 ) +- t25, 0.025 sqrt (s12 /n1 + s22 /n2)

= (97.66 - 97.22) +- 2.0595 * sqrt [0.792 /14 + 0.652 /15]

= (0.44) +- 2.0595 * 0.2697

= (-0.115, 0.995)

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