Question

You wish to test the following claim (H1) at a significance level of α=0.01.

      Ho:μ=50.6
      H1:μ<50.6

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

data
42.1
26.9
40.1
40.6
28.7
26.4
7.8
22.9
51.2

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 less than 50.6.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 50.6.
• The sample data support the claim that the population mean is less than 50.6.
• There is not sufficient sample evidence to support the claim that the population mean is less than 50.6.

Please explain how to do this problem on a TI-84 calculator. Thanks!!!

Answer 1

Sol:

in excel

find sample mean and sample standard devaition

then go to

TESTS> T TEST IN ti 83 calculator

From output

t=-4.334

p=0.0012

alpha=0.01

p<alpha

for critical value

here n=9

df=9-1=8

critical value in excel is

=T.INV(0.01;8)

=2.89646

critical value =-2.896

test statistic,t=-4.334

Reject Null hypothesis

Accept alternative hypothesis

The test statistic is...

• not in the critical region

• reject the null

• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 50.6.