Deck 9: One-Sample Hypothesis Tests

Question 1

The level of significance refers to the probability of making a Type II error.

Answer 1

False

Question 2

A Type I error can only occur if you reject H₀.

Answer 2

True

Question 3

For a given level of significance, the critical value of Student's t increases as n increases.

Answer 3

False

Question 4

In hypothesis testing, we cannot prove a null hypothesis is true.

Question 5

The probability of a false positive is decreased if we reduce α.

Question 6

Compared to using α = .01, choosing α = .001 will make it less likely that a true null hypothesis will be rejected.

Question 7

A two-tailed hypothesis test for H₀: μ = 15 at α = .10 is analogous to asking if a 90 percent confidence interval for μ contains 15.

Question 8

A hypothesis test may be statistically significant, yet have little practical importance.

Question 9

For a given level of significance (α), increasing the sample size will increase the probability of Type II error because there are more ways to make an incorrect decision.

Question 10

A false positive in a drug test for steroids is a Type II error.

Question 11

A Type II error can only occur when you fail to reject H₀.

Question 12

The level of significance refers to the probability of making a Type I error.

Question 13

When the probability of a Type I error increases, the probability of a Type II error must decrease, ceteris paribus.

Question 14

For a given sample size, reducing the level of significance will decrease the probability of making a Type II error.

Question 15

A simultaneous reduction in both α and β will require a larger sample size.

Question 16

John rejected H₀, so we know definitely that he did not commit a Type II error.

Question 17

The probability of rejecting a false null hypothesis increases as the sample size increases, other things being equal.

Question 18

If a judge acquits every defendant, the judge will never commit a Type I error. (H₀ is the hypothesis of innocence.)

Question 19

When your sample size increases, the chance of both Type I and Type II error will increase.

Question 20

For a given sample size and α level, the Student's t value always exceeds the z value.

Question 21

In a right-tailed test, the null hypothesis is rejected when the value of the test statistic exceeds the critical value.

Question 22

The p-value is the probability of the sample result (or one more extreme), assuming H₀ is true.

Question 23

A null hypothesis is rejected when the calculated p-value is less than the critical value of the test statistic.

Question 24

The probability of rejecting a true null hypothesis is the significance level of the test.

Question 25

The null hypothesis is rejected when the p-value exceeds the level of significance.

Question 26

In the hypothesis H₀: π = π₀, the value of π₀ is derived from the sample.

Question 27

For a sample of nine items, the critical value of Student's t for a left-tailed test of a mean at α = .05 is -1.860.

Question 28

In testing a proportion, normality of p can be assumed if nπ₀ ≥ 10 and n(1 - π₀) ≥ 10.

Question 29

Holding other factors constant, it is harder to reject the null hypothesis for a mean when conducting a two-tailed test rather than a one-tailed test.

Question 30

If the hypothesized proportion is π₀ = .025 in a sample of size 120, it is safe to assume normality of the sample proportion p.

Question 31

If the null and alternative hypotheses are H₀: μ ≤ 100 and H₁: μ > 100, the test is right-tailed.

Question 32

For a given null hypothesis and level of significance, the critical value for a two-tailed test is greater than the critical value for a one-tailed test.

Question 33

In testing the hypotheses H₀: π ≤ π₀, H₁: π > π₀, we would use a right-tailed test.

Question 34

For a given H_o and level of significance, if you reject the H₀ for a one-tailed test, you would also reject H₀ for a two-tailed test.

Question 35

Power is the probability of rejecting the null hypothesis when it is false and is equal to 1 - β.

Question 36

If we desire α = .10, then a p-value of .13 would lead us to reject the null hypothesis.

Question 37

The critical value of a hypothesis test is based on the researcher's selected level of significance.

Question 38

Other things being equal, a smaller standard deviation implies higher power.

Question 39

For a mean, we would expect the test statistic to be near zero if the null hypothesis is true.

Question 40

To test the hypothesis H₀: π = .0125 using n = 160, it is safe to assume normality of p.

Question 41

A power curve for a mean is at its lowest point when the true μ is very near μ₀.

Question 42

In hypothesis testing, we are trying to prove the null hypothesis.

Question 43

After testing a hypothesis, we decided to reject the null hypothesis. Thus, we are exposed to:

A)Type I error.
B)Type II error.
C)Either Type I or Type II error.
D)Neither Type I nor Type II error.

Question 44

In graphing power curves, there is a different power curve for each sample size n.

Question 45

Which of the following is correct?

A)When sample size increases, both α and β may decrease.
B)Type II error can only occur when you reject H₀.
C)Type I error can only occur if you fail to reject H₀.
D)The level of significance is the probability of Type II error.

Question 46

Which statement about α is not correct?

A)It is the probability of committing a Type I error.
B)It is the test's significance level.
C)It is the probability of rejecting a true H₀.
D)It is equal to 1 - β.

Question 47

Increasing the sample size shifts the power curve upward, ceteris paribus.

Question 48

A smaller probability of Type II error implies higher power of the test.

Question 49

The power curve plots β on the Y-axis and the test statistic on the X-axis.

Question 50

The height of the power curve shows the probability of accepting a true null hypothesis.

Question 51

The power of a test is the probability that the test will reject a false null hypothesis.

Question 52

Larger samples lead to increased power, ceteris paribus.

Question 53

Varying the true mean is a movement along the power curve, not a shift in the curve.

Question 54

Which of the following is incorrect?

A)The level of significance is the probability of making a Type I error.
B)Lowering both α and β at once will require a higher sample size.
C)The probability of rejecting a true null hypothesis increases as n increases.
D)When Type I error increases, Type II error must decrease, ceteris paribus.

Question 55

For a given sample size, when we increase the probability of a Type I error, the probability of a Type II error:

A)remains unchanged.
B)increases.
C)decreases.
D)is impossible to determine without more information.

Question 56

John rejected his null hypothesis in a right-tailed test for a mean at α = .025 because his critical t value was 2.000 and his calculated t value was 2.345. We can be sure that:

A)John did not commit a Type I error.
B)John did not commit a Type II error.
C)John committed neither a Type I nor Type II error.
D)John committed both a Type I and a Type II error.

Question 57

In hypothesis testing, we are trying to reject the alternative hypothesis.

Question 58

After testing a hypothesis regarding the mean, we decided not to reject H₀. Thus, we are exposed to:

A)Type I error.
B)Type II error.
C)Either Type I or Type II error.
D)Neither Type I nor Type II error.

Question 59

When σ is unknown, it is more conservative to use z instead of t for the critical value.

Question 60

Increasing the level of significance shifts the power curve upward, ceteris paribus.

Question 61

You are driving a van packed with camping gear (total weight 3,500 pounds including yourself and family) into a northern wilderness area. You take a "short cut" that turns into a one-lane road, with no room to turn around. After 11 miles you come to a narrow bridge with a faded sign saying, "Safe Up to 2 Tons." About a half-mile ahead, you can see that your road rejoins the main highway. You consider the sign's hypothesis carefully before making a decision. The cost of Type I error is:

A)you pass safely over the bridge and everyone's happy.
B)about $23,900, not including medical bills.
C)you will find out just how cold that river actually is.
D)your kids will think you're a chicken.

Question 62

Hypothesis tests for a mean using the critical value method require:

A)using a two-tailed test.
B)sampling a normal population.
C)knowing the true population mean.
D)specifying α in advance.

Question 63

Which is not true of p-values?

A)When they are small, we want to reject H₀.
B)They measure the probability of an incorrect decision.
C)They show the chance of Type I error if we reject H₀.
D)They do not require α to be specified a priori.

Question 64

For a right-tailed test of a hypothesis for a population mean with n = 14, the value of the test statistic was t = 1.863. The p-value is:

A)between .05 and .025.
B)between .10 and .05.
C)greater than .10.
D)less than .01.

Question 65

Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours. A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital and found a mean hospital stay of 40 hours with a standard deviation of 20 hours. "Aha!" she cried, "the average stay exceeds the guideline." At α = .025, the critical value for a right-tailed test of her hypothesis is:

A)1.753
B)2.131
C)1.645
D)1.960

Question 66

Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. In a left-tailed test at α = .05, which is the most accurate statement?

A)We would strongly reject the claim.
B)We would clearly fail to reject the claim.
C)We would face a rather close decision.
D)We would switch to α = .01 for a more powerful test.

Question 67

"My careful physical examination shows no evidence of any serious problem," said Doctor Morpheus. "However, a very costly lab test can be performed to check for the rare condition known as estomalgia fatalis. The test is almost invariably negative for persons with your age and symptoms. My personal hypothesis is that the occasional stomach pain you reported is due to indigestion caused by eating tacos with too much hot sauce. But you must decide for yourself." As you consider your doctor's hypothesis, what would be the consequence of Type I error on your part?

A)It can't be determined without knowing the type of test.
B)Your estomalgia fatalis will go undetected.
C)You will waste money on an unnecessary lab test.
D)Your survivors will enjoy a sizeable malpractice award.

Question 68

Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours. A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital, and found a mean hospital stay of 40 hours with a standard deviation of 20 hours. "Aha!" she cried, "the average stay exceeds the guideline." The p-value for a right-tailed test of her hypothesis is:

A)between .05 and .10.
B)between .025 and .05.
C)between .01 and .025.
D)less than .01.

Question 69

Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. To test DullCo's hypothesis, the test statistic is:

A)-1.980
B)-1.728
C)-2.101
D)-1.960

Question 70

As you are crossing a field at the farm, your country cousin Jake assures you, "Don't worry about that old bull coming toward us. He's harmless." As you consider Jake's hypothesis, what would be Type I error on your part?

A)You will soon feel the bull's horns.
B)You will run away for no good reason.
C)Jake will not have any more visits from you.

Question 71

The level of significance is not:

A)the probability of a "false rejection."
B)a value between 0 and 1.
C)the likelihood of rejecting the null hypothesis when it is true.
D)the chance of accepting a true null hypothesis.

Question 72

Which is not a likely reason to choose the z distribution for a hypothesis test of a mean?

A)The value of σ is known.
B)The sample size n is very large.
C)The population is normal.
D)The value of σ is very large.

Question 73

Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours. A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital and found a mean hospital stay of 40 hours with a standard deviation of 20 hours. "Aha!" she cried, "the average stay exceeds the guideline." The value of the test statistic for her hypothesis is:

A)2.080
B)0.481
C)1.866
D)2.000

Question 74

"I believe your airplane's engine is sound," states the mechanic. "I've been over it carefully, and can't see anything wrong. I'd be happy to tear the engine down completely for an internal inspection at a cost of $1,500. But I believe that roughness you heard in the engine on your last flight was probably just a bit of water in the fuel, which passed harmlessly through the engine and is now gone." As the pilot considers the mechanic's hypothesis, the cost of Type I error is:

A)the pilot will experience the thrill of no-engine flight.
B)the pilot will be out $1,500 unnecessarily.
C)the mechanic will lose a good customer.
D)impossible to determine without knowing α.

Question 75

The critical value in a hypothesis test:

A)is calculated from the sample data.
B)usually is .05 or .01 in most statistical tests.
C)separates the acceptance and rejection regions.
D)depends on the value of the test statistic.

Question 76

A study over a 10-year period showed that a certain mammogram test had a 50 percent rate of false positives. This indicates that:

A)about half the tests indicated cancer.
B)about half the tests missed a cancer that exists.
C)about half the tests showed a cancer that didn't exist.
D)about half the women tested actually had no cancer.

Question 77

For a test of a mean, which of the following is incorrect?

A)H₀ is rejected when the calculated p-value is less than the critical value of the test statistic.
B)In a right-tailed test, we reject H₀ when the test statistic exceeds the critical value.
C)The critical value is based on the researcher's chosen level of significance.
D)If H₀: μ ≤ 100 and H₁: μ > 100, then the test is right-tailed.

Question 78

After lowering the landing gear, the pilot notices that the "gear down and locked" light is not illuminated. "It's probably just a burned out light bulb," she says, as she proceeds on final approach for landing. Considering the pilot's hypothesis, which is the result of Type I error?

A)The sound of metal scraping on concrete will be heard upon landing.
B)The landing is delayed unnecessarily while the bulb and gear are checked.
C)We cannot be sure without knowing whether or not the bulb is actually faulty.

Question 79

Dullco Manufacturing claims that its alkaline batteries last at least 40 hours on average in a certain type of portable CD player. But tests on a random sample of 18 batteries from a day's large production run showed a mean battery life of 37.8 hours with a standard deviation of 5.4 hours. To test DullCo's hypothesis, the p-value is:

A)slightly less than .05.
B)exactly equal to .05.
C)slightly greater than .05.
D)uncertain without knowing α.

Question 80

Which of the following statements is correct?

A)Increasing α will make it more likely that we will reject H₀, ceteris paribus.
B)Doubling the sample size roughly doubles the test statistic, ceteris paribus.
C)A higher standard deviation would increase the power of a test for a mean.
D)The p-value shows the probability that the null hypothesis is false.