Question

A physiological experiment was conducted to study the effect of various factors on pulse rate. For one factor, there were 92 subjects, the mean pulse rate of which was 72.87, and the sample standard deviation was 11.01. Consider the following hypotheses: i. H0: m=75 vs. Ha: m> 75, ii. H0: m=75 vs. Ha: m does not =75 where m is the population mean. a). Compute the p-value for each test . b) State the conclusion based on the 5% level of significance.

Answer 1

(a)

(i)

H0: = 75

Ha: > 75

SE = s/

= 11.01/ = 1.1478

Test statistic is:

t = (72.87 - 75)/1.1478 = - 1.8557

One tail - Right Side Test

By Technology, p - value = 0.9584

(ii)

H0: = 75

Ha: 75

SE = s/

= 11.01/ = 1.1478

Test statistic is:

t = (72.87 - 75)/1.1478 = - 1.8557

Two Tail Test

By Technology, p - value = 0.0833

(b)

(i) For H0: = 75

         Ha: > 75:

Since calculated p - value = 0.9584 is greater than = 0.05, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data do not support the claim that Population mean is greater than 75.

(i) For H0: = 75

         Ha: 75:

Since calculated p - value = 0.0833 is greater than = 0.05, the difference is not significant. Fail to reject null hypothesis.

Conclusion:

The data do not support the claim that Population mean is different from 75.