Question

9. In order to test H_o: µ=20 versus H₁: µ<20, a simple random sample of size n=18 is obtained from a population that is known to be normally distributed. If x-bar=18.3 and s=4.3, compute the test statistics at the α=.05 level of significance and draw a t distribution with the appropriate area shaded. Should you reject the null?

THAN

In order to test H_o: µ=50 versus H₁: µ < 50, a simple random sample of size n =24 is obtained from a population that is known to be normally distributed.

a. If x-bar=47.1 and s=10.3, compute the test statistic.

b. If the researcher decides to test this hypothesis at the α=0.05 level of significance, determine the critical value.

c. Draw a t-distribution that depicts the critical region.

d. Will the researcher reject the null hypothesis? Why?

Answer 1

Solution:

9.

The null and alternative hypotheses are:

Under the null hypothesis, the test statistic is:

Now using the t table, the left-tailed t critical value at 0.05 significance level is:

We fail to reject the null hypothesis because the test statistic does not fall in the rejection region.

In order to test H_o: µ=50 versus H₁: µ < 50, a simple random sample of size n =24 is obtained from a population that is known to be normally distributed.

a. If x-bar=47.1 and s=10.3, compute the test statistic.

b. If the researcher decides to test this hypothesis at the α=0.05 level of significance, determine the critical value.

c. Draw a t-distribution that depicts the critical region.

d. Will the researcher reject the null hypothesis? Why?

Answer:

a. The test statistic is:

b. If the researcher decides to test this hypothesis at the α=0.05 level of significance, determine the critical value.

Answer: Now using the t table, the left-tailed t critical value at 0.05 significance level is:

c. Draw a t-distribution that depicts the critical region.

d. Will the researcher reject the null hypothesis? Why?

Answer: Fail to reject the null hypothesis, because the test statistic does not fall in the rejection region.