Question

	MALE	FEMALE
Count	28	21
Mean	72.8	72.4
Standard Deviation	5.3	7.7

A researcher wanted to see whether there was a significant difference in resting pulse rates for men and women. The data she collected is summarized to the right. For both groups, the data appear to be unimodal and symmetric. Is this evidence that resting pulse rates for men are higher than for women? Test an appropriate hypothesis using a significance level of 0.10 (? = 0.10). You can assume all conditions and assumptions are met.

a. Write the Hypothesis for the test. H0: HA:

b. Find the P-value. P-value:_______________

c. Give the conclusion in context. (3 things needed)

d. create a 90% confidence interval for the difference in mean resting pulse rates for men and women and interpret your interval in the context of the problem.

Answer 1

A researcher wanted to see whether there was a significant difference in resting pulse rates for men and women. The data she collected is summarized to the right. For both groups, the data appear to be unimodal and symmetric. Is this evidence that resting pulse rates for men are higher than for women? Test an appropriate hypothesis using a significance level of 0.10 (? = 0.10)

a. Write the Hypothesis for the test.

$\ H_0: \mu_1 = \mu_2 \ H_1: \mu_1 > \mu_2$

Upper tail test

b. Find the P-value. P-value: 0.4152

$t = \frac{\bar{x_1} - \bar{x_2}}{\sqrt{ \frac{(n_1 - 1) s_1^2 + (n_2 - 1) s_2^2} {(n_1 +n_2 -2)} *{(\frac{1}{n_1} + \frac{1}{n_2})}}}$

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data
Hypothesized Difference	0
Level of Significance	0.1
Population 1 Sample
Sample Size	28
Sample Mean	72.8
Sample Standard Deviation	5.3
Population 2 Sample
Sample Size	21
Sample Mean	72.4
Sample Standard Deviation	7.7
Intermediate Calculations
Population 1 Sample Degrees of Freedom	27
Population 2 Sample Degrees of Freedom	20
Total Degrees of Freedom	47
Pooled Variance	41.3666
Standard Error	1.8567
Difference in Sample Means	0.4000
t Test Statistic	0.2154
Upper-Tail Test
Upper Critical Value	1.2998
p-Value	0.4152
Do not reject the null hypothesis

c. Give the conclusion in context. (3 things needed)

since P value =0.4152 which is > 0.10 level of significance. Ho is not rejected.

There is not enough evidence that resting pulse rates for men are higher than for women.

d. create a 90% confidence interval for the difference in mean resting pulse rates for men and women and interpret your interval in the context of the problem.

$CI = ( \bar x_1 - \bar x_2) \pm t*se$

Confidence Interval Estimate
for the Difference Between Two Means
Data
Confidence Level	90%
Intermediate Calculations
Degrees of Freedom	47
t Value	1.6779
Interval Half Width	3.1154
Confidence Interval
Interval Lower Limit	-2.7154
Interval Upper Limit	3.5154

90% confidence interval for the difference in mean resting pulse rates for men and women is ( -2.7154, 3.5154).

We are 90% confident that true difference in mean resting pulse rates for men and women falls in the interval           ( -2.7154, 3.5154).