Question

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

      Ho:?=61.7
      Ha:?>61.7

You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size n=97n=97 with mean M=64M=64 and a standard deviation of SD=5.8SD=5.8.

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) ?? or greater than ??

This test statistic leads to a decision to...

reject the null, accept the null, or fail to reject the null

As such, the final conclusion is that...

A.) There is sufficient evidence to warrant rejection of the claim that the population mean is greater than 61.7.

B.) There is not sufficient evidence to warrant rejection of the claim that the population mean is greater than 61.7.

C.) The sample data support the claim that the population mean is greater than 61.7.

D.) There is not sufficient sample evidence to support the claim that the population mean is greater than 61.7.

Answer 1

a) The test statistic here is computed as:

Therefore 3.906 is the test statistic value here.

b) As this is a one tailed test, for n - 1 =96 degrees of freedom, we get form the t distribution tables, the p-value as:

p = P( t₉₆ > 3.906 ) = 0.0001

Therefore 0.0001 is the required p-value here.

c) The p-value here is 0.0001 < 0.001 which is the level of significance, Therefore p-value is less than

d) As the p-value is lower the test is significant and we reject the null hypothesis here.

e) As the test is significant,  The sample data support the claim that the population mean is greater than 61.7.