Question

Consider a sample of size 22 taken from a normal population. The sample mean is 2.777 and the sample standard deviation is 0.13. We test H_o: μ = 2.7 versus H₁: μ > 2.7 at the α = 0.05 level. The rejection region and our decision are

Select one:

a. t > 1.721; REJECT Ho

b. t > 2.080; REJECT Ho

c. t > 2.074; REJECT Ho

d. t > 1.717; REJECT Ho

Answer 1

In the above question, we have to do a t-test based on the given information.

where,

The t-statistic is:

given,

the sample mean

standard deviation

n = 22

then the degrees of freedom = (n - 1) = (22 -1) = 21

We can clearly see that the given test is one-tailed because we have to test only for right-tailed which is

Now, let us calculate the t-critical value:

which is calculated value.

Now,

Decision:

Reject Ho, If the calculated t-value is greater than tabulated t value.

Failed to reject Ho, if calculated t-value is less than tabulated t-value.

So, Here on looking at the t-table for the one-tailed test at 21 degrees of freedom we get tabulated value as 1.721.

Now, we can clearly see that the calculated t-value is greater than the tabulated t-value. Thus, we reject the Ho because .

The correct answer is (a.)

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