1.Test the null hypothesisH0:=3.6against the alternative hypothesisHA:3.6, based on a random sample of 37 observations drawn from a normally distributed population withx=3.8and =0.89.

a) What is the value of the test statistic?Round your response toat least 3 decimal places. b) What is the appropriate p-value?Round your response to at least3 decimal places.

c) Is the null hypothesis rejected at:

i) the 5% level of significance? YES or NO

ii) the 10% level of significance? YES or NO

2.Test the null hypothesisH0:=3.8against the alternative hypothesisHA:<3.8, based on a random sample of25 observations drawn from a normally distributed population withx=3.6and=0.68.

a) What is the value of the test statistic?Round your response toat least 3 decimal places.

b) What is the appropriate p-value?Round your response toat least 3 decimal places.

c) Is the null hypothesis rejected at:

i) the 10% level of significance? YES or NO

ii) the 5% level of significance? YES or NO

3.Suppose a hypothesis testofH0:=0is being carried out against the one-sided alternativeHA:<0at=0.1190. Assume that the population is normally distributed, and thatis known.

What is the appropriate rejection region?

A. Z-1.18

B. Z-1.18

C. Z-1.18

4.Suppose the null hypothesis ofH0:=0is being tested againstthe one-sided alternative hypothesisHA:<0, at the 5% level of significance. If a random sample of size 9 is taken, and the population is assumed to be normally distributed, what is the appropriate rejection region?

A. t-2.306

B. t1.96

C. t-2.306

D. t-1.860

E. t-1.860

5.Suppose the null hypothesis ofH0:=0is being tested againstthe two-sided alternative hypothesisHA:0in a population that is assumed to be normally distributed. If a random sample of size 12 is taken, and thettest statistic is calculated to bet= 2.58, then:

a) The p-value falls within which one of the following ranges:

A. p-value > 0.10

B. 0.05 < p-value < 0.10

C. 0.02 < p-value < 0.05

D. 0.01 < p-value < 0.02

E. p-value < 0.01

b)Is the null hypothesis rejected at the 5% level of significance? YES or NO

c) Is the null hypothesis rejected at the 1% level of significance? YES or NO

6.Suppose the null hypothesis ofH0:=0is being tested against a two-sided alternative hypothesis, at the 10% level of significance. If a random sample of size 25 is taken, and the population is assumed to be normally distributed, what is the appropriate rejection region?

A. t1.318

B. t1.318

C. t1.645

D. t1.711

E. t1.711

7.Suppose a random sample of size 22 is taken from a normally distributed population, and the sample mean and variance are calculated to bex=5.26ands^2=0.5respectively.

Use this information to test the null hypothesisH0:=5versus the alternative hypothesisHA:>5.

a) What is the value of the test statistic, for testing the null hypothesis that the population mean is equal to 5?Round your response to at least 3 decimal places.

b) The p-value falls within which one of the following ranges:

A. p-value > 0.10

B. 0.05 < p-value < 0.10

C. 0.025 < p-value < 0.05

D. 0.01 < p-value < 0.025

E. p-value < 0.01

c) i) Is the null hypothesis rejected at the 5% level of significance? YES or NO

ii) Is the null hypothesis rejected at the 1% level of significance? YES or NO

8.Suppose a hypothesis testofH0:=0is being carried out against a two-sided alternative hypothesis at=0.1. Assume that the population is normally distributed, and thatis known.

What is the appropriate rejection region?

A. Z1.645

B. Z1.645

C. Z1.645

D. Z1.96

E. Z1.96

9.A localnewscasterreports that the average rainfall in the month of June is approximately 92 mm. However, a meteorologist wishes to test this claim, believing that the average rainfall in June is actually higher than 92 mm. He collects data on the average June rainfall for 10 randomly selected years, and computes a mean of 95 mm. Assuming that the population standard deviation is known to be 19.0, and that rainfall is normally distributed, determine each of the following:

a) What are the appropriate hypotheses:

A. H0:X=92,HA:X>92

B. H0:=92,HA:92

C. H0:X=92,HA:X92

D. H0:=92,HA:>92

b) Calculate the appropriate test statistic.Round your answer toat least 3 decimal places.

c) What is the appropriate conclusion that can be made, at the 5% level of significance?

A. There is insufficient evidence to reject the null hypothesis, and therefore no significantevidence that the mean rainfall in June is different from92 mm.

B. There is sufficient evidence to reject the null hypothesis, and thereforeconclude that the mean rainfall in June is more than 92 mm.

10.Suppose a hypothesis test ofH0:=0is tested against the alternative hypothesisHA:<0, and the resultingZtest statistic isZ=1.32.

a) What is the appropriate p-value for the hypothesis test.Round your response toat least 4 decimal places.

b) Based on the p-value, would you reject the null hypothesis at the 10% level of significance? YES or NO