Question

the mean resting pulse rate of men is 76 beats per minute. a simple random sample of men who regularly work out at Mitch's gym is obtained and their resting pulse rates 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 76 beats per minute. assume that the standard deviation of the resting pulse rates of all men who workout at Mitch's gym is known to b 3.4 beats per minute. use the p value method of testing hypothesis.

81 68 75 82 93 87 59 89 93 66 98 63

Answer 1

Solution:
Given in the question
The claim is that these sample pulse rates come from a population with a mean less than 76 beats per minute So null and alternate hypothesis can be written as
Null hypothesis H0: = 76
Alternate hypothesis Ha: <76
The sample mean can be calculated as
Sample mean (Xbar)= (81 + 68 + 75 + 82 + 93 + 87 + 59 + 89 + 93 + 66 + 98 + 63)/12 = 954/12 = 79.5
Population standard deviation() = 3.4
Here we will use Z test as population standard deviation is known so test statistic value can be calculated as
Z = (Xbar - )//sqrt(n) = (79.5-76)/3.4/sqrt(12) = 3.57
At alpha = 0.05, and this is left tailed test so Zcritical value is -1.645, So
Decision Rule : Reject Null hypothesis, if Test statistic value is less than -1.645, else do not reject the null hypothesis.
Here we can see that test stat value is greater than test critical value (3.57>-1.645), so we are failed to reject the null hypothesis and we don't have significant evidence to support the claim is that these sample pulse rates come from a population with a mean less than 76 beats per minute