Question

You wish to test the following claim (HaHa) at a significance level of α=0.01α0.01.

      Ho:μ=58.9Hoμ58.9
      Ha:μ≠58.9Haμ58.9

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=22n22 with mean M=57.7M57.7 and a standard deviation of SD=8.1SD8.1.

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 58.9.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 58.9.
• The sample data support the claim that the population mean is not equal to 58.9.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 58.9.

Answer 1

Solution :

The null and alternative hypothesis is ,

= 58.9

M = 57.7

S = 8.1

n = 22

This will be a two tailed test because the alternative hypothesis is

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :   = 58.9

Ha :    58.9

Test statistic = z

= (M - ) /s / n

= ( 58.9 - 57.7 ) / 8.1 / 22

= 0.69

The test statistic = 0.69

Df = n - 1 = 22 - 1 = 21

P-value = 0. 4978

=0.01

0.4978 > 0.01

P-value >

P - value greater than α

Fail to Reject the null hypothesis .

There is not sufficient sample evidence to support the claim that the population mean is not equal to 58.9