A study was done on body temperatures and women. The results are shown in the ta

Question

A study was done on body temperatures and women. The results are shown in the table. Assume are independent simple 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. Test the claim that men have a higher mean body temperature than women. What are the null and alternative hypotheses? H_0: mu_1 greaterthanorequalto mu_2 H_1: mu_1

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: 1< 2

Alternative hypothesis: 1 > 2

Note that these hypotheses constitute a one-tailed test.

Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a two-sample t-test of the null hypothesis.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = sqrt[(s12/n1) + (s22/n2)]

SE = 0.2762

DF = 68

t = [ (x1 - x2) - d ] / SE

t = 0.58

where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between population means, and SE is the standard error.

The observed difference in sample means produced a t statistic of 0.58. We use the t Distribution Calculator to find P(t > 0.58) = 0.282

Interpret results. Since the P-value (0.282) is greater than the significance level (0.05), we cannot reject the null hypothesis.

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