Question

​Claim: The mean pulse rate​ (in beats per​ minute) of adult males is equal to 68.5 bpm. For a random sample of 162 adult​ males, the mean pulse rate is 69.9 bpm and the standard deviation is 11.3 bpm. Complete parts​ (a) and​ (b) below.

Answer 1

Let the random variable X is defined as

X : Pulse rate of adult males

Given :

: Mean pulse rate of adult males.

We have to test the claim that

Mean pulse rate of adult males is equla to 68.5 bpm.

i.e. Null Hypothesis -

against

Alternative Hypothesis - ( two-tailed test).

Since population standard deviation is unknown, we use one sample t-test for testing population mean.

The value of test statistic is

Value of test statistic t = 1.5759

Alpha: level of significance = 0.05

d.f. = n-1 = 162 -1 = 161

Since test is two-tailed and value of test statistic t is 1.5759

p-value is obtained by

Using R

> pvalue = 2 * (1- pt(1.5769,161))
> pvalue
[1] 0.1167814

pvalue = 0.1167.

Decision : Since pvalue > alpha, we failed to reject the null hypothesis.

Conclusion: There is sufficient evidence support to claim that Mean pulse rate of adult males is equla to 68.5 bpm.