Question

You wish to test the following claim (H1H1) at a significance level of α=0.002α=0.002.

      Ho:μ=57.7Ho:μ=57.7
      H1:μ≠57.7H1:μ≠57.7

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=98n=98 with mean M=60.9M=60.9 and a standard deviation of SD=7.7SD=7.7.

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 57.7.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 57.7.
• The sample data support the claim that the population mean is not equal to 57.7.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 57.7.

Answer 1

Solution :

= 57.7

M =60.9

S =7.7

n = 98

This is the two tailed test .

The null and alternative hypothesis is ,

H0 :    = 57.7

Ha :     57.7

Test statistic = t

= (M - ) / S / n

= (60.9 -57.7) / 7.7 / 98

= 4.114

Test statistic = t=  4.114

P-value =0.9999

= 0.02

P-value >

0.9999 > 0.02

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 57.7.