Question

BodyTemp 97.6 99.4 99 98.8 98 98.9 99 97.8 96.8 99 98.4 98.8 97.8 98.9 98.4 96.9 99.5 98.8 97.6 97.9 97.7 98.3 97.4 100.8 98.3 98.2 98 97.8 97.2 98.2 97.4 97.5 98.2 98 98.4 99.3 98.2 98.1 97.7 99 98.5 98.6 98.8 98.4 98.7 96.4 98 97.7 98.2 98.7	Pulse 69 77 75 84 71 76 81 77 75 81 82 78 71 80 70 74 75 83 74 76 77 79 78 77 78 69 89 74 64 73 72 70 57 67 73 68 64 67 61 79 83 78 64 81 78 69 73 84 72 73	Gender 0 1 0 1 0 1 0 1 1 1 0 0 1 0 0 0 0 1 0 0 0 1 0 1 1 1 1 0 0 1 0 0 1 0 1 1 1 0 1 0 1 0 1 1 0 1 1 1 0 0

2. Download the BodyTemp.MTW file from Canvas. We will be comparing the body temperatures of men and women.  [30 points]

A.Make a graph to compare the distributions of men and women’s body temperatures.

B. Use Minitab Express to determine if there is evidence that the mean body temperatures of men and women are different.  The coding of gender is 0=man and 1=woman. Assume that the distribution of the body temperature data is normal. Use the five-step hypothesis testing procedure and remember to include all relevant Minitab Express output. You should not need to do any hand calculations.

Step 1:Check assumptions and write hypotheses

Step 2: Calculate the test statistic

Step 3:Identify the pvalue

Step 4:Make a decision

Step 5:State a “real world” conclusion

Answer 1

A. Make a graph to compare the distributions of men and women’s body temperatures.

Here, we have to compare the distributions of men and women’s body temperatures by using histograms. Histograms are given as below:

From above histograms, it is observed that the distributions for men and women’s body temperatures are not same.

B. Use Minitab Express to determine if there is evidence that the mean body temperatures of men and women are different. The coding of gender is 0=man and 1=woman. Assume that the distribution of the body temperature data is normal. Use the five-step hypothesis testing procedure and remember to include all relevant Minitab Express output. You should not need to do any hand calculations.

Here, we have to use two sample t test for checking the given hypothesis. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H₀: There is no any significant difference in the average body temperatures of men and women.

Alternative hypothesis: H_a: There is a significant difference in the average body temperature of men and women.

H₀: µ₁ = µ₂ vs. H_a: µ₁ ? µ₂

This is a two tailed test.

We use 5% level of significance for this test. (? = 0.05)

The test statistic formula is given as below:

t = (X1bar – X2bar) / sqrt[(S₁² / n₁)+(S₂² / n₂)]

A Minitab output for this test is given as below:

Two-Sample T-Test and CI: BodyTemp, Gender

Two-sample T for BodyTemp

Gender       N      Mean     StDev   SE Mean

0           25    98.172     0.675      0.14

1           25    98.348     0.851      0.17

Difference = mu (0) - mu (1)

Estimate for difference: -0.176

95% CI for difference: (-0.614, 0.262)

T-Test of difference = 0 (vs not =): T-Value = -0.81 P-Value = 0.422 DF = 45

The p-value for this test is given as 0.422 which is greater than given level of significance or ? = 0.05.

So, we do not reject the null hypothesis that there is no any significant difference in the average body temperatures of men and women.

We conclude that there is insufficient evidence that the mean body temperatures of men and women are different.