Question

You wish to test the following claim (H1H1) at a significance level of α=0.01α=0.01.

      Ho:μ=79.5Ho:μ=79.5
      H1:μ<79.5H1:μ<79.5

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=637n=637 with mean ¯x=79x¯=79and a standard deviation of s=10.3s=10.3.

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 less than 79.5.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 79.5.
• The sample data support the claim that the population mean is less than 79.5.
• There is not sufficient sample evidence to support the claim that the population mean is less than 79.5.

Answer 1

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 79 - 79.5 ) / ( 10.3 / √(637) )
t = -1.2252

Test Criteria :-
Reject null hypothesis if t < -t(α, n-1)
t(α, n-1) = t(0.01 , 637-1) = 2.332
t > -t(α, n-1) = -1.2252 > - 2.332
Result :- Fail to reject null hypothesis

Decision based on P value
P - value = P ( t > 1.2252 ) = 0.1105
Reject null hypothesis if P value < α = 0.01 level of significance
P - value = 0.1105 > 0.01 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

t = -1.225

P - value = P ( t > 1.2252 ) = 0.1105

greater than α

fail to reject the null

There is sufficient evidence to warrant rejection of the claim that the population mean is less than 79.5.