Answer:
a) Null hypothesis:
Alternative hypothesis:
This hypothesis test is a left tailed test.
b) 
The p value for this case can be calculated with this probability:
We can conduct the test with the Ti84 using the following steps:
STAT>TESTS>T-test>Stats
We input the value 
and for the alternative we select 
. Then press Calculate.
And we got the same results.
Step-by-step explanation:
Information given
represent the sample mean
represent the population standard deviation
sample size
represent the value to test
represent the significance level for the hypothesis test.
t would represent the statistic
represent the p value for the test
Part a) System of hypothesis
We want to test if the true mean is less than 3, the system of hypothesis would be:
Null hypothesis:
Alternative hypothesis:
This hypothesis test is a left tailed test.
Part b
The statistic is given by:
(1)
Replacing the info given we got:
The p value for this case can be calculated with this probability:
We can conduct the test with the Ti84 using the following steps:
STAT>TESTS>T-test>Stats
We input the value and for the alternative we select . Then press Calculate.
And we got the same results.
