Deck 9: A: large-Sample Tests of Hypotheses

Question 1

How is a Type II error is committed?

A) by rejecting a true null hypothesis
B) by rejecting a false null hypothesis
C) by not rejecting a true null hypothesis
D) by not rejecting a false null hypothesis

Answer 1

D

Question 2

Consider testing the hypothesis . If the value of the test statistic is equal to 1.36, then what is the p-value?

A) 0.1738
B) 0.2066
C) 0.4131
D) 0.9131

Answer 2

A

Question 3

If we reject the null hypothesis, what are we concluding?

A) that there is not enough statistical evidence to infer that the alternative hypothesis is true
B) that there is enough statistical evidence to infer that the alternative hypothesis is true
C) that there is enough statistical evidence to infer that the null hypothesis is true
D) that the test is statistically insignificant at whatever level of significance the test was conducted

Answer 3

B

Question 4

In testing the hypothesis , the following information is known: n = 64, = 78, and = 10. In this case, what is the value of the test statistic?

A) +2.4
B) +1.96
C) -1.96
D) -2.4

Question 5

If we do NOT reject the null hypothesis, what are we concluding?

A) that there is not enough statistical evidence to infer that the alternative hypothesis is true
B) that there is enough statistical evidence to infer that the alternative hypothesis is true
C) that there is enough statistical evidence to infer that the null hypothesis is true
D) that the test is statistically insignificant at whatever level of significance the test was conducted

Question 6

In a two-tailed test for the population mean, the null hypothesis will be rejected at level of significance if which of the following conditions holds for the value of the test statistic z?

A) | z | >
B) | z | < -
C) -< z <
D) | z | > z

Question 7

There is a close connection between Type I errors, Type II errors, and the power of a test. Which of the following statements is NOT true of those interrelationships?

A) The probability of committing a Type II error increases as the probability of committing a Type I error decreases.
B) The probability of committing a Type II error and the level of significance are the same.
C) The power of the test decreases as the level of significance decreases.

Question 8

Which of the following is an example of a null hypothesis?

A) This industrial process makes windshields having an average length equal to 33 inches.
B) The average quantity of detergent put into a box by this filling machine is not 1 pound.
C) This shipping company's average delivery time is different from 3 days.
D) The average thickness of aluminum sheets is not 0.03 inches, as required.

Question 9

If a hypothesis is rejected at the 0.05 level of significance, what can be deduced from that?

A) The hypothesis must be rejected at any level.
B) The hypothesis must be rejected at the 0.02 level.
C) The hypothesis must not be rejected at the 0.02 level.
D) The hypothesis may or may not be rejected at the 0.02 level.

Question 10

Which of these terms is a proposition which is tentatively advanced as being possibly true?

A) an acceptance region
B) a confidence level
C) a hypothesis
D) a p-value

Question 11

Which of the following p-values will lead us to reject the null hypothesis if the level of significance 0.05?

A) 0.025
B) 0.05
C) 0.10
D) 0.20

Question 12

A government testing agency studies aspirin capsules to see if they contain less medication than advertised. Suppose the testing agent concludes the capsules contain a mean amount below the advertised level when in fact the advertised level is the true mean. Which type of error, if any, did the testing agency commit?

A) This is a Type I error.
B) This is a Type II error.
C) This is a correct decision.
D) It is impossible to answer this question.

Question 13

In a criminal trial, when is a Type I error committed?

A) when a guilty defendant is acquitted
B) when an innocent person is convicted
C) when a guilty defendant is convicted
D) when an innocent person is acquitted

Question 14

In hypothesis testing, to what does the term "critical value" refer?

A) the probability, 1 -, of avoiding the Type I error of erroneously rejecting a null hypothesis that is in fact true
B) the value of a test statistic that divides all possible values into an acceptance region and a rejection region
C) any sample result that leads to the continued acceptance of the null hypothesis because it has a high probability of occurring when the null hypothesis is true
D) the probability, 1 -, of avoiding the Type II error of erroneously accepting a null hypothesis that is in fact false

Question 15

In a two-tailed test, if the p-value is less than the probability of committing a Type I error, what can you conclude?

A) A one-tailed test should be used.
B) The null hypothesis should be rejected.
C) The null hypothesis should not be rejected.
D) Another sample should be selected at random from the population.

Question 16

A quality control officer tests bottles of shampoo to see if the filling machines are putting the proper amount in each bottle. After testing a sample of bottles, the quality control officer decides to leave the filling machines operating. However, the filling machines are not operating properly. Which type of error, if any, did the quality control officer commit?

A) This is a Type I error.
B) This is a Type II error.
C) This is a correct decision.
D) This is an incorrect decision.

Question 17

What is the first step in hypothesis testing?

A) formulating two opposing hypotheses, called the null and the alternative hypotheses
B) selecting a test statistic
C) calculating the p-value
D) determining the rejection region

Question 18

When is a Type I error committed?

A) when we reject a true null hypothesis
B) when we reject a false null hypothesis
C) when we don't reject a false null hypothesis
D) when we don't reject a true null hypothesis

Question 19

What is the p-value of a test?

A) It is the smallestat which the null hypothesis can be rejected.
B) It is the largestat which the null hypothesis can be rejected.
C) It is the smallestat which the null hypothesis cannot be rejected.
D) It is the largestat which the null hypothesis cannot be rejected.

Question 20

If you wish to determine there is evidence that the average starting salary for finance graduates exceeds $42,000, how would you formulate the null and alternative hypotheses?

A) so that either a two-tailed or one-tailed test could be used
B) so that a two-tailed test should be used
C) so that a one-tailed test should be used
D) so that the probability of committing a Type II error would be equal to 0.42

Question 21

If a hypothesis test is to be conducted using = 0.025, what does that imply about the test?

A) There is a 2.5% chance that the null hypothesis is true.
B) There is a maximum 2.5% chance that a false null hypothesis will be rejected.
C) There is a maximum 2.5% chance that a true null hypothesis will be rejected.
D) There is 2.5% chance of committing a Type I error and 97.5% chance of committing a Type II error.

Question 22

What would be the lower limit of a confidence interval, at the 95% level of confidence, for the population proportion if a sample of size 200 had 40 successes?

A) 0.2554
B) 0.2465
C) 0.1535
D) 0.1446

Question 23

In testing vs. a random sample of size 200 produced a sample proportion Given these results, what is the approximate p-value of the test?

A) 0.0384
B) 0.0768
C) 0.4616
D) 0.5384

Question 24

Assuming that all necessary conditions are met, what needs to be changed in the formula so that we can use it to construct a confidence interval estimate for the population proportion p?

A) Theshould be replaced by p.
B) Theshould be replaced by.
C) Theshould be replaced by.
D) Theshould be replaced by.

Question 25

When testing vs. , the observed value of the z-score was found to be -2.15. What would the p-value for this test be?

A) 0.0158
B) 0.0316
C) 0.9684
D) 0.9842

Question 26

If you wish to construct a confidence interval estimate for the difference between two population means, what would an increase in the sample sizes used result in?

A) a decrease in the critical value z
B) a narrower confidence interval
C) a wider confidence interval
D) a confidence interval that contains 0

Question 27

Suppose that we reject the null hypothesis at the 0.05 level of significance. For which of the following -values do we also reject the null hypothesis?

A) 0.02
B) 0.04
C) 0.06

Question 28

In testing vs. the test statistic value z is found to be 1.69. What is the p-value of the test?

A) 0.0455
B) 0.0910
C) 0.1977
D) 0.3023

Question 29

If you wish to estimate the difference between two population means using two independent large samples, the 90% confidence interval estimate can be constructed using which of the following critical values?

A) 2.33
B) 1.96
C) 1.645
D) 1.28

Question 30

Two independent samples of sizes 40 and 50 are randomly selected from two populations to test the difference between the population means . Which of the following best describes the sampling distribution of the sample mean difference ?

A) It is normally distributed.
B) It is approximately normal.
C) It is student t-distributed with 88 degrees of freedom.
D) It is student t-distributed with 90 degrees of freedom.

Question 31

What is the rejection region for testing at the 0.05 level of significance?

A) |z| < 1.28
B) |z| > 1.96
C) z > 1.645
D) z < 2.33

Question 32

In testing the difference between two population means using two independent samples, the population standard deviations were assumed to be known and the calculated test statistic equalled 2.56. If the test was two-tailed and a 5% level of significance had been specified, what would be the most appropriate conclusion from the findings?

A) to reject the null hypothesis
B) not to not reject the null hypothesis
C) to choose two other independent samples
D) to accept the null hypothesis

Question 33

If the probability of committing a Type I error for a given test is to be decreased, then for a fixed sample size n, what will happen?

A) The power of the test will increase.
B) The probability of committing a Type II error will increase.
C) The probability of committing a Type II error will decrease.
D) A two-tailed test must be used.

Question 34

When testing vs. , the observed value of the z-score was found to be -2.15. Which of the following is the p-value for this test?

A) 0.0158
B) 0.0316
C) 0.9684
D) 0.9842

Question 35

Which of the following conditions must hold before one can make use of the standard normal distribution for constructing a confidence interval estimate for the population proportion p?

A) and) are both greater than 5, wheredenotes the sample proportion
B) np and n(1 - p) are both greater than 5
C) n(p +) and n(p -) are both greater than 5, wheredenotes the sample proportion
D) the sample size is greater than 5

Question 36

In formulating the null and alternative hypotheses, which of the following would be an acceptable null hypothesis?

A) The population mean is greater than 20.
B) The population mean is smaller than 20.
C) The population mean is equal to 20.
D) The population mean is equal to 0.

Question 37

The necessary conditions having been met, a two-tailed test is being conducted to test the difference between two population means, but your statistical software provides only a one-tail area of 0.036 as part of its output. What is the p-value for this test?

A) 0.009
B) 0.018
C) 0.072
D) 0.964

Question 38

In selecting the sample size to estimate the population proportion p, if we have no knowledge of even the approximate values of the sample proportion , what should we do?

A) take another sample and estimate
B) take two more samples and find the average of their's
C) let= 0.50
D) let= 0.95

Question 39

When testing vs. , the observed value of the z-score was found to be -2.15. What is the p-value for this test?

A) 0.0158
B) 0.0316
C) 0.9684
D) 0.9842

Question 40

In testing vs. which of the following would happen if the sample size were increased?

A) The sampling distribution of the sample meanwould have the same variability.
B) There would be no effect on the level of significance for the test.
C) This would have an effect on whether the null hypothesis is true or not.

Question 41

A survey claims that 9 of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative, that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. What is the approximate value of the test statistic in this ?

A) -2.33
B) -1.86
C) -1.67
D) -0.14

Question 42

A sample of size 100 selected from one population has 60 successes, and a sample of size 150 selected from a second population has 95 successes. In this case, what is the test statistic for testing the equality of the population proportions?

A) -0.5319
B) -0.419
C) 0.2702
D) 0.7293

Question 43

In testing the null hypothesis , if is false, which of the following errors could the test lead to?

A) a Type I error
B) a Type II error
C) a Type III error
D) a Type IV error

Question 44

As the significance level $\alpha$ increases, the probability of a Type I error increases and the size of the rejection region increases.

Question 45

The p-value of a statistical test measures the actual risk of committing a Type I error.

Question 46

In constructing a confidence interval estimate for the difference between two population proportions, what is the most appropriate option?

A) Pool the population proportions when the populations are normally distributed.
B) Pool the population proportions when the population means are equal.
C) Pool the population proportions when they are equal.
D) Never pool the population proportions to construct a confidence interval for.

Question 47

A two-tail test is a test in which a null hypothesis can be rejected by an extreme result occurring in only one direction.

Question 48

For a fixed sample size n, as the probability of a Type II error $\beta$ decreases, the probability of a Type I error $\alpha$ increases.

Question 49

Which of the following would be an appropriate null hypothesis to test a proportion?

A) The sample proportion is equal to 0.60.
B) The population proportion is greater than 0.60.
C) The population proportion is equal to 0.60.
D) The population proportion is not equal to 0.60.

Question 50

Which of the following would be an appropriate alternative hypothesis to test a proportion?

A) The population proportion is less than 0.65.
B) The sample proportion is less than 0.65.
C) The population proportion is equal to 0.65.
D) The sample proportion is equal to 0.65.

Question 51

A Type I error for a statistical test is committed if we reject the null hypothesis when it is true.

Question 52

A sample of size 150 from population 1 has 40 successes. A sample of size 250 from population 2 has 30 successes. What is the value of the test statistic for testing the null hypothesis that the proportion of successes in population one exceeds the proportion of successes in population two by 0.05?

A) 1.645
B) 1.960
C) 1.977
D) 2.327

Question 53

For testing the difference between two population proportions, under what circumstances should the pooled proportion estimate be used to compute the value of the test statistic?

A) when the populations are normally distributed
B) when the sample sizes are small
C) when the samples are independently drawn from the populations
D) when the null hypothesis states that the two population proportions are equal

Question 54

A Type I error is represented by , and is the probability of not rejecting a false null hypothesis.

Question 55

From a sample of 400 items, 14 are found to be defective. In this case, what is the point estimate of the population proportion defective?

A) 0.035
B) 0.05
C) 14
D) 28.57

Question 56

A Type II error for a statistical test is committed if we do not reject the null hypothesis when it is false.

Question 57

If the power of a statistical test is 0.9207, then the probability of accepting a false null hypothesis is 0.0793.

Question 58

The p-value of a statistical test is the largest value of the significance level for which the null hypothesis can be rejected.

Question 59

Which of the following is a required condition for using the normal approximation to the binomial in testing the difference between two population proportions?

A) and
B) and
C) and
D) and

Question 60

The necessary conditions having been met, a two-tailed test is being conducted to test the difference between two population proportions. If the value of the test statistic is 2.05, what is the p-value?

A) 0.4798
B) 0.2399
C) 0.0404
D) 0.0202

Question 61

The null hypothesis is a vehicle for making startling new claims that contradict the conventional wisdom, that assert "guilt without a reasonable doubt."

Question 62

A two-tailed test of hypothesis for a population mean with a significance level equal to 0.05 will have a critical value z equal to 0.475.

Question 63

In a hypothesis test, if the null hypothesis has been rejected, then it is impossible that a Type II error has been committed.

Question 64

A hypothesis that specifies a single value for the unknown parameter is called a point estimate.

Question 65

The p-value in hypothesis testing equals the probability, 1 - , of avoiding the Type I error of erroneously rejecting a null hypothesis that is in fact true.

Question 66

A p-value is a statistic computed from a simple random sample taken from the population of interest in a hypothesis test and then used for establishing the probable truth or falsity of the null hypothesis.

Question 67

In order to calculate the p-value associated with a test, it is necessary to know the level of significance .

Question 68

A set consisting of values that support the alternative hypothesis and lead to rejecting the null hypothesis is called the rejection region.

Question 69

A hypothesis that specifies a range of values for the unknown parameter is called an interval estimate.

Question 70

Reducing the probability of a Type I error also reduces the probability of a Type II error.

Question 71

In a one-tailed test, the larger the significance level , the larger the critical value will be.

Question 72

A professor of mathematics refutes the claim that the average student spends 4.5 hours studying for the final comprehensive exam. To test the claim, she should use the hypothesis , .

Question 73

In hypothesis testing, the decision to "accept" the null hypothesis is the same as the decision to "fail to reject" the null hypothesis.

Question 74

The necessary conditions having been met, a two-tailed test is being conducted to test the difference between two population means, but your statistical software provides only a one-tail area of 0.156 as part of its output. The p-value for this test will be 0.078.

Question 75

In a one-tailed test, the p-value is found to be equal to 0.036. If the test had been two-tailed, the p-value would have been 0.072.

Question 76

If the null hypothesis, H₀, cannot be corroborated in a hypothesis test, is tentatively embraced, which calls for action; thus, one can think of as the action hypothesis.

Question 77

If H₀ is corroborated in a hypothesis test, no action need be taken by anyone.

Question 78

If you wish to conduct a hypothesis test using a small significance level , you should increase your sample size to lower the probability of making a Type II error.

Question 79

Hypothesis testing is a systematic approach to assessing tentative beliefs about reality, which involves confronting those beliefs with evidence and deciding, in light of this evidence, whether the beliefs can be maintained as reasonable or must be discarded as untenable.

Question 80

In hypothesis testing, the statement of the null hypothesis always contains the equality sign.