Question

1. Find the critical t-value(s) for a one sample t-test given: α = 0.01 n = 12 one-tailed test (lower-tailed critical region)

a. 2.130 and -2.130

b. 3.103 and -3.103

c.-2.718

d. -2.567

e. 2.998

2.

Find the critical t-value(s) for a one sample t-testgiven:

α = 0.05

df = 26

one-tailed test (upper-tailed critical region)

a. 2.042 and -2.042

b.-1.812

c. 1.706

d. 3.241

e. -1.339

3. What decision you would make regarding the null hypothesis (reject or fail to reject (i.e., retain)) given the following scenario in a one sample t-test?

α = 0.05

p value = 0.022

a. reject the null hypothesis

b. fail to reject the null hypothesis

4. What decision you would make regarding the null hypothesis (reject or fail to reject (i.e., retain)) given the following scenario in a one sample t-test?

α = 0.01

p value = 0.524

a. reject the null hypothesis

b. fail to reject the null hypothesis

5. What decision you would make regarding the null hypothesis (reject or fail to reject (i.e., retain)) given the following scenario in a one sample t-test?

α = 0.01

p value = 0.005

a. reject the null hypothesis

b. fail to reject the null hypothesis

6. What decision you would make regarding the null hypothesis (reject or fail to reject (i.e., retain)) given the following scenario in a one sample t-test?

α = 0.05

p value = 0.232

a. reject the null hypothesis

b. fail to reject the null hypothesis

Answer 1

1. The critical value for T-distribution is calculated using the T table shown below at 0.01 level of significance and Degree of freedom=n-1=12-1=11.

So, The critical value for the left tailed test is

c.-2.718

Computed using T -table is shown below

2. Again the critical t-value for a one-sample t-test given at α = 0.05 df = 26 is computed using T table shown below as:

c. 1.706

Computed using the T -table is shown below

3. At  α = 0.05 where p-value = 0.022 is computed by testing. Since P-value <0.05 for a one-sample test hence,

a. reject the null hypothesis

4. For a one-sample t-test and at α = 0.01 p-value = 0.524, since the P-value >0.01 the level of significance for a one-tailed test

b. fail to reject the null hypothesis

5. in a one-sample t-test at level of significance α = 0.01 where p value = 0.005 thus Decision for One-tailed test :

a. reject the null hypothesis, because of the P-value <0.01.

6. In a one-sample t-test at α = 0.05 where p value calculated = 0.232 thus for a one-sample T-test the decision will be:

b. fail to reject the null hypothesis, Because of P-value >0.05

The T-table used for P-value calculation is: