1) Answer the following questions.

a) Define null and alternative hypotheses, and give an example of each.

b) What is meant by type error? A type 2 error? How are they related?

c) What is meant by the critical region? The Non-critical region?

d) When you are testing hypotheses by using proportions, what are the necessary requirements?

e) What is level of significance? How level of significance is related to P-value.

f) Explain the difference between a One-tailed and Two-tailed test

g) Give three examples of proportions.

h) Why is a proportion considered a binomial variable?

i) What are the mean and standard deviation of propertion

2) Using the Z table (Table E), find the critical value(s) for each.

a) = 0,05, two-tailed test

b) = 0,01, left-tailed test

c) = 0,005, right-tailed test

d) = 0,01, right-tailed test

e) = 0,05, left-tailed test

3) For each conjecture, state the null and alternative hypothesis.

a) The average age of community college students is 24.6 years

b) The average income of accountants is $51,497.00

c) The average age of attorneys is greater than 24.4 years

d) The average score of high school basket-ball game is less than 88

4) State weather the null hypothesis should be rejected on the basis of the given P-value. (6 Points)

a) P-value = 0.258, = 0,05, one-tailed test

b) P-value = 0.0684, = 0,10, two-tailed test

c) P-value = 0.0153, = 0,01, one-tailed test

d) P-value = 0.0232, = 0,05, two-tailed test

e) P-value = 0.002, = 0,01, one-tailed test

5) An insurance agent says that the mean cost of injuring a two-year-old sedan (in good condition) is less than $1200. A random sample of 7 similar insurance quotes has a mean cost $1125 and a standard deviation of $55. Is there enough evidence to support the agents claim at = 0.10? Assume the population is normally distributed. (20 points)

a) Identify the claim and state H and H

b) Identify the level of significance a and the degree of freedom.

c) Find out the critical value t and identify the rejection region.

d) Find the standardized test statistics t. Sketch a graph.

e) Decide whether to reject the null hypothesis.

f) Interpret the decision in the context of the original claim.

6) Speeding ticket Costs Average cost of speeding ticket plus court fee is approximately $150.00. Random sample of 38 speeding ticket court-cases showed that mean cost was $150.59. At the 0.01 level of significance is that greater than $150? The population standard deviation is $10.78

a) State hypotheses and identify the claim

b) Find the critical values

c) Compute the test value

d) Make the decision and summarize the results

7) A sporting goods manufacturer claims that the variance of strengths of certain fishing line is 15.9. A random sample of 15 fishing lines spools has a variance of 21.8. At a = 0,05, is there enough evidence to reject the manufacturers claims? Assume the population is normally distributed. (20 points)

a) Identify the claim and state H and H

b) Identify the level of significance a and the degree of freedom

c) Find out critical values [X] and [X] and identify the rejection regions.

d) Find the standardized test statistics X

e) Decide whether to reject the null hypothesis. Use a graph if necessary.

f) Intercept the decision in the context of the original claims.

8) Carbohydras in fast foods Number of carbohydras found in a random sample of fast food entrees listed. Is this sufficient evidence to conclude that the variance differs from 100? Use the 0.05 level of significance.

53 46 39 39 30

47 38 73 43 41

9) Operating Costs of an Automobile- The average cost of owning and operating an automobile is $1821 per 15000 miles including fixed and variable costs. Random survey of 40 automobile owners reviled an average cost of $8350 with population standard deviation of $750. Is there sufficient evidence to conclude that the average is greater than $8121? Use = 0.01

a) State hypotheses and identify the claim

b) Find the critical values

c) Compute the test value

d) Make the decision and summarize the results

10) Test the claim that the standard deviation of the number of air crafts stolen each year in the united State is less than 15. If a random sample of 12 years had a standard deviation of 13.6. Use = 0,05 (18 points)

a) Find the critical values

b) Compute the test value

c) Make the decision and summarize the results