Answer:
Step-by-step explanation:
a) H0: μ = 10
Ha: μ ≠ 10
This is a two tailed test
n = 13
Since α = 0.01, the critical value is determined from the t distribution table. Recall that this is a two tailed test. Therefore, we would find the critical value corresponding to 1 - α/2 and reject the null hypothesis if the absolute value of the test statistic is greater than the value of t 1 - α/2 from the table.
1 - α/2 = 1 - 0.01/2 = 1 - 0.005 = 0.995
The critical value is 3.012
The rejection region is area > 3.012
b) Ha: μ > 10
This is a right tailed test
n = 23
α = 0.1
We would reject the null hypothesis if the test statistic is greater than the table value of 1 - α
1 - α = 1 - 0.1 = 0.9
The critical value is 1.319
The rejection region is area > 1.319
c) Ha: μ > 10
This is a right tailed test
n = 99
α = 0.05
We would reject the null hypothesis if the test statistic is greater than the table value of 1 - α
1 - α = 1 - 0.05 = 0.95
The critical value is 1.66
The rejection region is area > 1.66
d) Ha: μ < 10
This is a left tailed test
n = 11
α = 0.1
We would reject the null hypothesis if the test statistic is lesser than the table value of 1 - α
1 - α = 1 - 0.1 = 0.9
The critical value is 1.363
The rejection region is area < 1.363
e) H0: μ = 10
Ha: μ ≠ 10
This is a two tailed test
n = 20
Since α = 0.05, we would find the critical value corresponding to 1 - α/2 and reject the null hypothesis if the absolute value of the test statistic is greater than the value of t 1 - α/2 from the table.
1 - α/2 = 1 - 0.05/2 = 1 - 0.025 = 0.975
The critical value is 2.086
The rejection region is area > 2.086
f) Ha: μ < 10
This is a left tailed test
n = 77
α = 0.01
We would reject the null hypothesis if the test statistic is lesser than the table value of 1 - α
1 - α = 1 - 0.01 = 0.99
The critical value is 2.376
The rejection region is area < 2.376
, where I is the identity matrix (1s on the diagonal, 0s elsewhere)
