Question

PLEASE EXPLAIN HOW TO DO ON TI-84

You wish to test the following claim (HAHA) at a significance level of α=0.02α=0.02.

      Ho:μ=54.2Ho:μ=54.2
      HA:μ≠54.2HA:μ≠54.2

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

data
41.7
40.8
40.8
76.1
71.1
60.1
44
46
50.1
56.1

What is the critical value for this test?  (Round to the thousandths)
critical value = ±±


Enter the data into L1 and make sure to use the "Data" option in T-Test.

What is the test statistic for this sample?  (Round to the thousandths)
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 54.2.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is not equal to 54.2.
• The sample data support the claim that the population mean is not equal to 54.2.
• There is not sufficient sample evidence to support the claim that the population mean is not equal to 54.2

Answer 1

Critical value

area = 0.9900

df = degree of freedom = n - 1 = 10 - 1 = 9

Now follow the path of the TI - 84 for the critical value

Press " 2ND " .....> Press " VARS" ......>select"invT

Area = 0.99

df = 9

press " enter "

You get the critical value as 2.8214

Our test is two tailed test because H_a Contains not equal to sign

So the critical value has sign and round to 3 decimal place

Answer : Critical value =

Follow the path of the TI - 84

Press " STAT ......> Select " EDIT " .......> select " Edit " ......> Select " L1 "

Enter the given data one by one in L1

Here we use the T test because population standard deviation is not known

Press " STAT " .......> select " TEST " .......>Select " T Test ......> select "Data "

List : L1   ( For the L1 press 2ND and then press " 1 " )

Freq : 1

Then select " calculate "

Press " enter "

t = test statistics = -0.3743246934

p = p value = 0.7168299497

What is the test statistic for this sample?  

Answer :Test statistics = - 0 .374

The test statistic is.Not in the critical region

( Because -.2.821 < -0.374 < 2.821    and the critical region is < -2.821    and > 2.821 )

Decision rule

- critical value < Test statistics < +critical value ( Then we Fail to reject H₀ )

Otherwise we reject H₀

so the decision is " Fail to reject the Null "

Conclusion

There is sufficient evidence to warrant rejection of the claim that the population mean is not equal to 54.2.