1.

If the absolute value of the calculated test statistic for a hypothesis is greater than the critical value of the test statistic (taken from the statistical table), then:

A) do not reject the null hypothesis

B) reject the null hypothesis

2.

If the p-value of a statistical test of a hypothesis is 0.065 and the level of significance selected for the hypothesis is 0.05, then

A) do not reject the null hypothesis

B) reject the null hypothesis

3.

As the selected level of significance, α, gets smaller (i.e. .005 is smaller than .05), then

A) the region of rejection of the null hypothesis gets smaller

B) the level of confidence in the rejection of the null hypothesis increases (assuming that the null is rejected)

C) Both of the above

D) None of the above

4.

If an economist wishes to determine whether there is evidence that the average family income in a community earns more than $45,000

A) Either a one-tail or two-tail test could be used with equivalent results.

B) A one-tail test is used.

C) A two-tail test is used.

D) None of the above.

5.

A Type II error occurs when the null hypothesis is accepted (not rejected) when it actually is false.

A) True

B) False

6.

One would use a t-statistic instead of a z-statistic in hypothesis tests about the mean of a single population

A) If the sample set is large.

B) If the population standard deviation and sample standard deviation is known.

C) If only the sample standard deviation is known.

D) In all cases.

7.

The manager of a paint supply store wants to determine whether the amount of paint contained in 1-gallon cans purchased from a nationally known manufacturer actually averages 1-gallon. The manufacturers specifications indicate a standard deviation in the amount of paint equal to 0.02 gallon. A random sample of 50 cans is selected, and the mean amount of paint in the 1-gallon can is found to be 0.995 gallons. Which of the following indicates the appropriate test statistic, critical value of the test statistic, and decision if one uses a = 0.01 to test if the mean amount of paint is less than 1-gallon?

A) z = -0.25, z-critical = -2.33, Content not less than 1 gallon.

B) z = -1.77, z-critical = -2.33, Content not less than 1 gallon.

C) z = -1.77, z-critical = -2.33, Content less than 1 gallon.

D) z = -1.77, z-critical = -2.58, Content not less than 1 gallon.

E) z = -1.77, z-critical = -2.58, Content less than 1 gallon.

8.

Referring to the content of question 7, which of the following indicates the appropriate test statistic, critical value of the test statistic, and decision if one uses a = 0.01 to test if the mean amount of paint is different than 1-gallon?

A) z = -0.25, z-critical = -2.33, Content not less than 1 gallon.

B) z = -1.77, z-critical = -2.33, Content not less than 1 gallon.

C) z = -1.77, z-critical = -2.33, Content less than 1 gallon.

D) z = -1.77, z-critical = -2.58, Content not different than 1 gallon.

E) z = -1.77, z-critical = -2.58, Content different than 1 gallon.

Situation 1:

The manager of Pepperoni Pizza Restaurant is running an experiment to test the changes in consumer satisfaction as the restaurant moved from an old-style pizza to a new-style pizza. Consumers were asked to rate their preferences on a scale from -10 to +10, where negative ratings favor the old style pizza and positive values favor the new style pizza. The ratings for 40 randomly selected customers are used for the test about preferences. Answer questions 9 and 10 using this information.

9.

The summary statistics from the sample of 40 consumers indicate a sample mean of 2.10 and a sample standard deviation of 4.717. The positive sample means provides some evidence in favor of improved consumer preferences but given the rather large value of the standard deviation, does it provide enough evidence to suggest a DIFFERENCE in preferences? Which of the following indicates the appropriate test statistic, critical value of the test statistic, and decision if one uses á = 0.05 to test if the mean claim is DIFFERENT than 0.

A) t = 2.815, t-critical = 1.684, Consumer preference different.

B) t = 2.425, t-critical = 1.684, Consumer preferences Different.

C) t = 2.815, t-critical = 2.021, Consumer preferences Different.

D) t = 2.425, t-critical = 2.021, Consumer preferences Different.

E) t = 2.815, t-critical = 2.423, Consumer preferences NOT Different.

10.

The summary statistics from the sample of 40 consumers indicate a sample mean of 2.10 and a sample standard deviation of 4.717. The positive sample means provides some evidence in favor of improved consumer preferences but given the rather large value of the standard deviation, does it provide enough evidence to suggest an IMPROVEMENT in preferences? Which of the following indicates the appropriate p-value and conclusion if one uses á = 0.01 to test if the mean preference is GREATER THAN 0?

A) p-value =.0002; Preferences are Improved.

B) p-value = .003; Preferences are Improved.

C) p-value = .007; Preferences are Improved.

D) p-value = .016; Preferences are Improved.

E) p-value = .016, Preferences are NOT Improved.

11.

Developers of a new artificial heart found 6 defective hearts in a random sample of 400 of their manufactured hearts. What is the sample proportion of defective hearts?

A) 0.015

B) 0.025

C) 0.050

D) 0.125

12.

FDA approval for artificial hearts requires that fewer than 2% of the hearts can be defective. Suppose you are testing the null hypothesis H0: p = 0.02 against the alternative hypothesis H1: p < 0.02 at the level of significance a = 0.05 for the hearts described in question 11, which of the following indicates the appropriate test statistic, critical value of the test statistic, and FDA decision? (Hint: test of proportions)

A) z = .005/.00005 = 100; z-critical = 1.645, Defects less than 2%, Accept for Use.

B) z = .005/.00005 = 100; z-critical = 1.96, Defects not less than 2%, Do not accept for Use.

C) z = .005/.007 = 0.71; z-critical = 1.645, Defects less than 2%, Accept for Use

D) z = .005/.007 = 0.71; z-critical = 1.645, Defects not less than 2%, Do not accept for Use.

E) z = .005/.007 = 0.71; z-critical = 1.96, Defects not less than 2%, Do not accept for Use.

 

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