Question

/courses/1631958/q 2791378/take D Question 5 12 pts Pulse Rates of Men. A simple random sample of 40 men results in a standard deviation of 10.3 beats per minute (based on the data set provided). The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal range, the result is a standard deviation of 10 beats per minute. Use the sample results with 0.05 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Upload your work demonstrating all 5 completed steps for the hypothesis test. Your 5 steps should match the steps in the example posted in the lab introduction. (same as last week) There is not enough evidence to support the claim that the pulse rates of men have a standard deviation of 10 bpm. O O There is enough evidence to support the claim that the pulse rates of men have a standard d eviation of 10 bpm. here is not enough evidence to reject the claim that the pulse rates of men have a standard deviation of 10 bpm. O T O There is enough evidence to reject the claim that the pulse rates of men have a standard deviation of 1 0 bpm. 12 pts D Question 6 畢喧] @ e嬲自.豳 17 2

Answer 1

Question 5

To Test :-  

H0 :-   $\sigma^2 = 100$

H1 :-   $\sigma^2 \neq 100$

$\alpha = 0.05$
n = 40

Test Statistic :-
$\chi ^2 = ( (n-1) S^2) / \sigma^2$
$\chi ^2 = ( ( 40-1 ) * 106.09 ) / 100$
$\chi ^2 = 41.3751$
Test Criteria :-
Reject null hypothesis if $\chi ^2 > \chi_{\alpha/2, n - 1}^{2} ) OR \chi ^2 < \chi_{1 - \alpha/2, n - 1}^{2} )$
$\chi_{0.05/2,40 - 1}^{2} = 58.12$
$\chi_{0.05/2,40 - 1}^{2} = 23.654$
41.3751 lies between the value 58.12 and 23.654 , hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = 2 * P ( $\chi ^2$ > 41.3751 )
P value = 0.7348
Reject null hypothesis if P value < $\alpha = 0.05$
Since P value = 0.7348 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is enough evidence to support the claim that the pulse rate for men have a standard deviation of 10 bpm.

Question 6

To Test :-  

H0 :-   $\sigma^2 = 100$

H1 :-   $\sigma^2 \neq 100$

$\alpha = 0.05$
n = 40

Test Statistic :-
$\chi ^2 = ( (n-1) S^2) / \sigma^2$
$\chi ^2 = ( ( 40-1 ) * 134.56 ) / 100$
$\chi ^2$ = 52.4784

Test Criteria :-
Reject null hypothesis if $\chi ^2 > \chi_{\alpha/2, n - 1}^{2} ) OR \chi ^2 < \chi_{1 - \alpha/2, n - 1}^{2} )$
$\chi_{0.05/2,40 - 1}^{2} = 58.12$
$\chi_{0.05/2,40 - 1}^{2} = 23.654$
52.4784 lies between the value 58.12 and 23.654 , hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

Decision based on P value
P value = 2 * P ( $\chi ^2$ > 52.4784 )
P value = 0.1464
Reject null hypothesis if P value < \alpha
Since P value = 0.1464 > 0.05, hence we fail to reject the null hypothesis
Conclusion :- We Fail to Reject H0

There is enough evidence to support the claim that the pulse rate for women have a standard deviation of 10 bpm.