Question

1) Given the the null hypothesis for this test is

Ho: μ > x̅ and the significance level for the test is α = .05

What is(are) the critical value(s) Z*(α) for accepting/rejecting the null hypothesis? (2 decimals)

2)

Given the the null hypothesis for this test is

Ho: μ > x̅ and the significance level for the test is α = .01

What is(are) the critical value(s) Z*(α) for accepting/rejecting the null hypothesis? (2 decimals)

3)

Given the the null hypothesis for this test is

Ho: μ > x̅ and the significance level for the test is α = .1

What is(are) the critical value(s) Z*(α) for accepting/rejecting the null hypothesis? (2 decimals)

4)

Given the the null hypothesis for this test is

Ho: μ < x̅ and the significance level for the test is α = .1

What is(are) the critical value(s) Z*(α) for accepting/rejecting the null hypothesis? (2 decimals)

5)

Given the the null hypothesis for this test is

Ho: μ < x̅ and the significance level for the test is α = .05

What is(are) the critical value(s) Z*(α) for accepting/rejecting the null hypothesis? (2 decimals)

6)

Given the the null hypothesis for this test is

Ho: μ < x̅ and the significance level for the test is α = .01

What is(are) the critical value(s) Z*(α) for accepting/rejecting the null hypothesis? (2 decimals)

7)

Given the the null hypothesis for this test is

Ho: μ ≠  x̅ and the significance level for the test is α = .1

What is(are) the critical value(s) Z*(α) for accepting/rejecting the null hypothesis? (2 decimals)

8)

Given the the null hypothesis for this test is

Ho: μ ≠  x̅ and the significance level for the test is α = .05

What is(are) the critical value(s) Z*(α) for accepting/rejecting the null hypothesis? (2 decimals)

9)

Given the the null hypothesis for this test is

Ho: μ ≠ x̅ and the significance level for the test is α = .05 with n = 10 observations

What is(are) the critical value(s) t*(α,df) for accepting/rejecting the null hypothesis? (2 decimals)

10)

Given the the null hypothesis for this test is

Ho: μ ≠ x̅ and the significance level for the test is α = .05 with n = 50 observations

What is(are) the critical value(s) t*(α,df) for accepting/rejecting the null hypothesis? (2 decimals)

11)

Given the the null hypothesis for this test is

Ho: μ ≠ x̅ and the significance level for the test is α = .05 with n = 100 observations

What is(are) the critical value(s) t*(α,df) for accepting/rejecting the null hypothesis? (2 decimals)

Answer 1

Solution:-) Here, z-value is taken from normal probability table. For one-tailed Z value is taken at  α while for two tailed test Z-value is taken at α/2 .

1) Ho: μ > x̅ vs  H_a: μ < x̅ , and the significance level for the test is α = .05. Here alternative hypotheses is left tailed test , therefore the critical value of  Z_(α) is 1.645 for reject/accept the null hypothesis

2) Ho: μ > x̅ vs  H_a: μ < x̅ , and the significance level for the test is α = .01. Here alternative hypotheses is left tailed test , therefore the critical value of  Z_(α) is 2.326 for reject/accept the null hypothesis

3) Ho: μ > x̅ vs  H_a: μ < x̅ , and the significance level for the test is α = .1. Here alternative hypotheses is left tailed test , therefore the critical value of  Z_(α) is 1.282 for reject/accept the null hypothesis

In all the above cases, if Z_(α) < calculated Z, then reject the null hypothesis, otherwise accept.

4) Ho: μ < x̅ vs  H_a: μ > x̅ , and the significance level for the test is α = .05. Here alternative hypotheses is left tailed test , therefore the critical value of  Z_(α) is 1.645 for reject/accept the null hypothesis

5) Ho: μ < x̅ vs  H_a: μ > x̅ , and the significance level for the test is α = .01. Here alternative hypotheses is left tailed test , therefore the critical value of  Z_(α) is 2.326 for reject/accept the null hypothesis

6) Ho: μ < x̅ vs  H_a: μ >x̅ , and the significance level for the test is α = .1. Here alternative hypotheses is left tailed test , therefore the critical value of  Z_(α) is 1.282 for reject/accept the null hypothesis

In all the above cases, if Z_(α) > calculated Z, then reject the null hypothesis, otherwise accept.

7) Ho: μ ≠  x̅ vs  H_a: μ = x̅ , it is two tailed test and the significance level for the test is α = .1. Here alternative hypotheses is left tailed test , therefore the critical value of  Z_(α) is 1.645 for reject/accept the null hypothesis

8) Ho: μ ≠  x̅ vs  H_a: μ = x̅ , it is two tailed test and the significance level for the test is α = .05. Here alternative hypotheses is left tailed test , therefore the critical value of  Z_(α) is 1.96 for reject/accept the null hypothesis

9) Ho: μ ≠ x̅ vs H_a: μ = x̅ and the significance level for the test is α = .05 with n = 10 observations

the critical value(s) t*(0.05,9) is 1.83

10) Ho: μ ≠ x̅ vs H_a: μ = x̅ and the significance level for the test is α = .05 with n = 50 observations

the critical value(s) t*(0.05,49) is : 1.67

11) Ho: μ ≠ x̅ vs H_a: μ = x̅ and the significance level for the test is α = .05 with n = 100 observations

the critical value(s) t*(0.05,99) is 1.66