Question

Evan is using a one-sample ?t‑test to test the null hypothesis ?0:?=48H0:μ=48 against the alternative ?1:?≠48H1:μ≠48. A simple random sample of size 11 is used for the test.

Determine the positive and negative critical values of the test statistic ?t that will reject the null hypothesis at significance level ?=0.05α=0.05. Round your answers to three decimal places.

-t = t =

Alejandra is using a one-sample ?t‑test to test the null hypothesis ?0:?=10.0H0:μ=10.0 against the alternative ?1:?<10.0H1:μ<10.0 using a simple random sample of size ?=15n=15. She requires her results to be statistically significant at level ?=0.05α=0.05. Determine the maximum value of ?t that will reject this null hypothesis.

t =

Answer 1

Question 1

We are given

α = 0.05

n = 11

df = n - 1 = 10

So, critical values by using t-table are given as below:

-t = - 2.228

t = 2.228

Question 2

We are given

α = 0.05

n = 15

df = n - 1 = 14

So, critical values by using t-table are given as below:

t = 1.761