Question

Test the given claim. Use the P-value method or the traditional method as indicated. Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s) or P-value, conclusion about the null hypothesis, and final conclusion that addresses the original claim.

The mean resting pulse rate for women is 72 beats per minute. A simple random sample of women who regularly work out at the local gym is obtained and their resting pulse rates (in beats per minute) are listed below. Use a 0.05 significance level to test the claim that these sample pulse rates come from a population with a mean less than 72 beats per minute.

Assume that the standard deviation of the resting pulse rates of all women who worked out at the local gym is known to be 6.6 beats per minute. Use the traditional method of testing hypotheses.

54 59 69 84 74 64 69 70 66 80 59 71 76 63

Answer 1

Here we have given that,

Claim: To check whether the Sample pulse rates come from a population with mean less than 72 beats per minute.

The Hypothesis is as follows

Ho:μ = 72

v/s

H1 :μ< 72

This is Left (one) tailed test as our interest is to show population with mean less than 72 beats per minute.

We have given that,

Xi: Pulse rate of women

Xi
54
59
69
84
74
64
69
70
66
80
59
71
76
63

n= Number of observation = 14

= sample mean =68 bpm

we have population standard deviation known

= population standard deviation of women who work out at local gym =6.6 bpm

Now, we can find the test statistic

z – statistics =

=

68-72

= -2.27

we get,

the Test statistic is -2.27

Now we find the P-value

= level of significance=0.05

Now, we can find the P-value

P-value =(P(Z < z) as this is left one tailed test

= P( Z < -2.27)

= 0.0116 using standard normal z probability table

we get the P-value is 0.0116

Decision:

P-value < 0.05 ()

That is we reject Ho (Null Hypothesis)

Conclusion

There is the sufficient evidence that the Sample pulse rates come from a population with mean less than 72 beats per minute.