Q3: A sample of 72 observations has a mean of 107 and a population standard deviation of 8. A second sample of 86 observations has a mean of 104 and a population standard deviation of 10. Assume that each sampled population is normally distributed and conduct a z-test of hypothesis using a 0.04 significance level. H0: 1 = 2 H1: 1 2

a) What type of test is this?

A one-tailed test.

A two-tailed test.

None of the above.

b) What is the correct decision rule?

Reject H0 in favour of H1 if the computed value of the statistic is less than -2.05 or greater than 2.05.

Reject H0 in favour of H1 if the computed value of the statistic is between -2.05 and 2.05.

Reject H0 in favour of H1 if the computed value of the statistic is less than 2.05.

Reject H0 in favour of H1 if the computed value of the statistic is greater than 2.05.

Reject H0 in favour of H1 if the computed value of the statistic is less than -1.75 or greater than 1.75.

Reject H0 in favour of H1 if the computed value of the statistic is between -1.75 and 1.75.

None of the above.

c) Compute the value of the test statistic. at least two decimal places.

d) What is your decision regarding H0?

There is sufficient evidence, at the given significance level, to reject H0, and accept H1.

There is insufficient evidence, at the given significance level, to reject H0.

There is insufficient evidence to reject or not reject the null hypothesis.

e) Calculate the p-value. at least four decimal places.

Question 4:

A sample of 47 observations has a mean of 99 and a population standard deviation of 7. A second sample of 58 has a mean of 96 and a population standard deviation of 9. Conduct a z-test about a difference in sample means using a 0.01 significance level and the following hypotheses: H0: 1 - 2 = 0 H1: 1 - 2 0

a) What is the correct decision rule?

Reject H0 in favour of H1 if the computed value of the statistic is less than 2.58.

Reject H0 in favour of H1 if the computed value of the statistic is greater than 2.58.

Reject H0 in favour of H1 if the computed value of the statistic is less than -2.33 or greater than 2.33.

Reject H0 in favour of H1 if the computed value of the statistic is between -2.33 and 2.33.

Reject H0 in favour of H1 if the computed value of the statistic is less than -2.58 or greater than 2.58.

Reject H0 in favour of H1 if the computed value of the statistic is between -2.58 and 2.58.

None of the above.

b) Compute the value of the test statistic. at least two decimal places.

c) What is your decision regarding H0?

There is sufficient evidence, at the given significance level, to reject H0, and accept H1 or at least there is not enough evidence to reject H1.

There is insufficient evidence, at the given significance level, to reject H0.

There is insufficient evidence to reject or not reject the null hypothesis.

d) Calculate the p-value.at least four decimal places.