Question

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

      Ho:μ=71.3Ho:μ=71.3
      H1:μ>71.3H1:μ>71.3

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=33n=33 with mean M=78.3M=78.3 and a standard deviation of SD=18.3SD=18.3.

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 greater than 71.3.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.3.
• The sample data support the claim that the population mean is greater than 71.3.
• There is not sufficient sample evidence to support the claim that the population mean is greater than 71.3.

Answer 1

Test Statistic :-
t = ( X̅ - µ ) / (S / √(n) )
t = ( 78.3 - 71.3 ) / ( 18.3 / √(33) )
t = 2.197

P - value = P ( t > 2.1974 ) = 0.0177

Reject null hypothesis if P value < α = 0.01 level of significance
P - value = 0.0177 > 0.01 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

P value is greater than α

This test statistic leads to a decision to...

• fail to reject the null

Conclusion :-  There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 71.3.