9.5 Hypothesis Testing for Mean Unknown Using the Critical Value and Rejection Region (t-test)

You wish to test the following claim (H

a

H

a

) at a significance level of

=

0.01

=

0.01

.

H

o

:

=

79.8

H

o

:

=

79.8

H

a

:

<

79.8

H

a

:

<

79.8

You believe the population is normally distributed, but you do not know the standard deviation. You obtain asampleof sizen

=

39

n

=

39

with a mean of

x

=

x

=

74.7 and a standard deviation ofs

=

17.8

s

=

17.8

.

a.) This test is

left-tailed

right-tailed

two-tailed

b.) At

=

=

0.01, the critical value =(use 3 decimal places)

c.) The test statistic =(use 2 decimal places)

d.) The test statistic is...

• in the critical region
• not in the critical region

e.) This test statistic leads to a decision to...

• reject the null hypothesis
• accept the null hypothesis
• fail to reject the null hypothesis

f.) As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the population mean is less than 79.8.
• There is not sufficient evidence to warrant rejection of the claim that the population mean is less than 79.8.
• The sample data support the claim that the population mean is less than 79.8.
• There is not sufficient sample evidence to support the claim that the population mean is less than 79.8.