Question

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

      Ho:?=76.4Ho:?=76.4
      Ha:??76.4Ha:??76.4

You believe the population is normally distributed, but you do not know the standard deviation. You obtain the following sample of data:

data
80.9
83.6
77.8
82.2
73.9
89.9
81.5
75.8
63.1

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value = ±±

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

The test statistic is...

in the critical region
not in the critical region

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 76.4.
There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 76.4.
The sample data support the claim that the population mean is not equal to 76.4.
There is not sufficient sample evidence to support the claim that the population mean is not equal to 76.4.

Answer 1

Given data

population mean

number of sample talken (n)=9

Sum of the sample

sample mean   

Sum of the squere for the sample difference from mean

Variance

Sample Standard daviation

Now the hypothesis is

'

Now Z criticle value from the Standard table of probablity distribution for two tailed test at is

Test static form the formula we have

Since it is a two tailed test so criticle range is form -2.576 to +2.576

since -2.576<0.3323<+2.576

so we can say that   the test static is in the criticle region

Decision :--

Since test static lies in the criticle region so we can say that we

Fail to reject the null hypothesis

Conclusion:---

As we fail to reject the null hypothesis which says that the Population mean is equal to 76.4 so we can say that the conclusion of this hypothesis will be

There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 76.4.