Answer:
(a) Null Hypothesis, :
= 10 beats per minute
Alternate Hypothesis, :
10 beats per minute
(b) The value of chi-square test statistics is 35.704.
(c) P-value = 0.4360.
(d) We conclude that the pulse rates of men have a standard deviation equal to 10 beats per minute.
Step-by-step explanation:
We are given that a simple random sample of 36 men from a normally distributed population results in a standard deviation of 10.1 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.
Let = <u><em>population standard deviation for the pulse rates of men</em></u>.
(a)
So, Null Hypothesis, :
= 10 beats per minute {means that the pulse rates of men have a standard deviation equal to 10 beats per minute}
Alternate Hypothesis, :
10 beats per minute {means that the pulse rates of men have a standard deviation different from 10 beats per minute}
The test statistics that will be used here is <u>One-sample chi-square test</u> for standard deviation;
T.S. = ~
where, s = sample standard deviation = 10.1 beats per minute
n = sample of men = 36
So, <u><em>the test statistics</em></u> = ~
= 35.70 4
(b) The value of chi-square test statistics is 35.704.
(c) Also, the P-value of the test statistics is given by;
P-value = P( > 35.704) = <u>0.4360</u>
(d) Since the P-value of our test statistics is more than the level of significance as 0.4360 > 0.10, so <u><em>we have insufficient evidence to reject our null hypothesis</em></u> as the test statistics will not fall in the rejection region.
Therefore, we conclude that the pulse rates of men have a standard deviation equal to 10 beats per minute.