17. In a pulse rate research, a simple random sample of 625 men results in a mea

Question

17. In a pulse rate research, a simple random sample of 625 men results in a mean of 80 beats per minute, and a standard deviation of 11.5 beats per minute. Based on the sample results, the researcher concludes that the pulse rates of men have a standard deviation less than 12 beats per minutes. Use a 0.05 significance level to test the researcher’s claim.
(a) Identify the null hypothesis and alternative hypothesis.
(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
(c) Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.

(D)Is there sufficient evidence to support the researcher’s claim? Explain

Explanation / Answer

(a) Null Hypothesis : H0 : The pulse rates of men have a standard deviation equal or above 12 beats per minutes. >= 12 beats per minutes.

ALternative Hypothesis : Ha : THe  pulse rates of men have a standard deviation less than 12 beats per minutes. < 12 beats per minutes.

(b) Here sample standard deviation s = 11.5 beats per minute

0 = 12 beats per minute

n = 625

Here we will use chi-square test statistic.

X2 = (n -1) (s/ 0)2 = (625 - 1) (11.5/12)2 = 573.08333

Here dF = 624 and alpha = 0.05

so critcal test statistic

X2 critical = X2624,0.05 = 567.0512

(c) p- value = CHIDIST (X2 > 573.08333 ; dF = 624) = 0.0843 > 0.05

so yes we cannot reject the null hypothesis and can reject the resercher's claim that THe  pulse rates of men have a standard deviation less than 12 beats per minutes.

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