Question

You wish to test the following claim (HaHa) at a significance level of α=0.001α=0.001.

      Ho:μ=69.5Ho:μ=69.5
      Ha:μ≠69.5Ha:μ≠69.5

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=26n=26 with mean M=67.8M=67.8 and a standard deviation of SD=17.2SD=17.2.

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 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 not equal to 69.5.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 69.5.
• The sample data support the claim that the population mean is not equal to 69.5.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 69.5.

Answer 1

This is the two tailed test .

The null and alternative hypothesis is

H₀ :   = 69.5

H_a : 69.5

Test statistic = t

= ( - ) / s / n

= (67.8 - 69.5) /17.2 / 26

Test statistic = -0.50

P(z < -0.50) = 0.3085

P-value = 0.6170

= 0.001

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 69.5.