Question

Hypothesis Test for a Population Mean (σσ is Unknown)

You wish to test the following claim (HaHa) at a significance level of α=0.10α=0.10.

      Ho:μ=77.2Ho:μ=77.2
      Ha:μ≠77.2Ha:μ≠77.2

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=83n=83 with mean M=78.9M=78.9 and a standard deviation of SD=13.7SD=13.7.

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

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) αα

greater than αα

This test statistic 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 not equal to 77.2.

There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 77.2.

The sample data support the claim that the population mean is not equal to 77.2.

There is not sufficient sample evidence to support the claim that the population mean is not equal to 77.2.

Answer 1

The statistical software output for this problem is:

One sample T summary hypothesis test:
μ : Mean of population
H₀ : μ = 77.2
H_A : μ ≠ 77.2

Hypothesis test results:

Mean	Sample Mean	Std. Err.	DF	T-Stat	P-value
μ	78.9	1.5037704	82	1.1304918	0.2616

Hence,

Test statistic = 1.130

p-value = 0.2616

The p-value is greater than α

fail to reject the null

There is not sufficient sample evidence to support the claim that the population mean is not equal to 77.2.