A study was done on body temperatures of men and women. The results are shown in

Question

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, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.05

significance level for both parts.

a. Test the claim that men have a higher mean body temperature than women.

What are the null and alternative hypotheses?

b. What is the test statistic, t?

c. What is the p value?

d. What is the confidence interval?

Explanation / Answer

Question a)

Null Hypothesis (Ho): µ1 µ2

Alternative Hypothesis (Ha): µ1 > µ2

Question b)

t = ( x1 bar – x2 bar )/ SE (x1-x2)

x1 bar = 97.62

x2 bar = 97.38

s1 = 0.81
s2 = 0.63

n1 = 11

n2 = 59

SE (x1-x2) = ((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2) * (1/n1+1/n2)

                  = (((11-1)*0.81^2)+((59-1)*0.63^2))/(11+59-2) * ((1/11)+(1/59))

                  = 0.2166

t = (97.62 – 97.38) / 0.2166 = 1.108

Answer : Test statistics, t = 1.108

Question c)

We use excel function to find the p-value

p-value = TDIST(1.108,68,1)= 0.1359

Answer: 0.1359

Question d)

Confidence Interval:

(x1 bar – x2 bar ) (-/+) E

E = tc *SE

We find the critical value for 5% level of significance as 1.668

E = 1.668 * 0.2166 = 0.3613

0.24 (-/+) 0.3613

-0.121 and 0.601

Answer: -0.121 and 0.601

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