Question

Suppose we want to test  H₀ :  μ ≥ 30 versus  H₁ :  μ < 30. Which of the following possible sample results based on a sample of size 54 gives the strongest evidence to reject  H₀ in favor of  H₁?

a. x= 32,  s = 4

b. x=29,  s = 10

c. x= 28,  s = 16

d. x= 25,  s = 6

Answer 1

a)


The test hypothesis is


Now, the value of test static can be found out by following formula:

Since the sample size is n = 54, degrees of freedom on the t-test statistic are n-1 = 54-1 = 53
This implies that

Since, the t distribution is symmetric about zero, so
Since ,
we fail to reject the null hypothesis

b)


The test hypothesis is

Now, the value of test static can be found out by following formula:

Since the sample size is n = 54, degrees of freedom on the t-test statistic are n-1 = 54-1 = 53
This implies that

Since, the t distribution is symmetric about zero, so
Since , we fail to reject the null hypothesis

c)


The test hypothesis is


Now, the value of test static can be found out by following formula:


Since the sample size is n = 54, degrees of freedom on the t-test statistic are n-1 = 54-1 = 53
This implies that

Since, the t distribution is symmetric about zero, so
Since , we fail to reject the null hypothesis

d)


The test hypothesis is


Now, the value of test static can be found out by following formula:


Since the sample size is n = 54, degrees of freedom on the t-test statistic are n-1 = 54-1 = 53
This implies that

Since, the t distribution is symmetric about zero, so
Since ,
we reject the null hypothesis in favor of the alternative hypothesis