Question

You wish to test the following claim ( H a ) at a significance level of ? = 0.001 . H o : ? = 61.8 H a : ? < 61.8 You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n = 27 with mean M = 57 and a standard deviation of S D = 10.4 . What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value = The p-value is... less than (or equal to) ? greater than ? This p-value leads to a decision to... reject the null accept the null fail to reject the null As such, the final conclusion is that... There is sufficient evidence to warrant rejection of the claim that the population mean is less than 61.8. There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 61.8. The sample data support the claim that the population mean is less than 61.8. There is not sufficient sample evidence to support the claim that the population mean is less than 61.8.

Answer 1

The statistical software output for this problem is:

One sample T summary hypothesis test:
? : Mean of population
H₀ : ? = 61.8
H_A : ? < 61.8

Hypothesis test results:

Mean	Sample Mean	Std. Err.	DF	T-Stat	P-value
?	57	2.0014809	26	-2.3982242	0.012

Hence,

p - value = 0.0120

p - value is greater than ?.

Fail to reject the null

p - value > 0.001 so we do not reject the null hypothesis.

There is not sufficient sample evidence to support the claim that the population mean is less than 61.8.

Option D is correct.