Deck 10: Hypothesis Testing

Question 1

A test statistic is computed from sample data in hypothesis testing and is used in making a decision about whether or not to reject the null hypothesis.

Answer 1

True

Question 2

The larger the p-value, the more we doubt the null hypothesis.

Answer 2

False

Question 3

When the null hypothesis is not rejected, there is no possibility of making a Type I error.

Answer 3

True

Question 4

We are testing H₀: μ ≤ 8; versus H_A: μ > 8. Given α = .01, n = 25, = 8.112, and s = .16, we should reject the H₀. Assume that the population from which the sample is selected is normally distributed.

Question 5

We are testing H₀: μ ≥ 22; versus H_A: μ < 22. Given α = .01, n = 100, = 21.431, and σ = 1.295, we should not reject H₀.

Question 6

When applying either the critical value rule or the p-value rule about a single mean, other relevant factors held constant, increasing the level of significance, α, from .05 to .10 will reduce the probability of a Type II error.

Question 7

As the level of significance, α, increases, we are more likely to reject the null hypothesis.

Question 8

The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. She uses a z test to test the null hypothesis that the mean tensile strength is less than or equal to 800 pounds per square inch. The calculated z test statistic is a positive value that leads to a p-value of .067 for the test. If the significance level for this test is .10, the null hypothesis would be rejected.

Question 9

A Type II error is failing to reject a false null hypothesis.

Question 10

You cannot make a Type II error when the null hypothesis is true.

Question 11

A Type I error is rejecting a true null hypothesis.

Question 12

The manager of the quality department for a tire manufacturing company wants to know the average tensile strength of rubber used in making a certain brand of radial tire. The population is normally distributed and the population standard deviation is known. She uses a z test to test the null hypothesis that the mean tensile strength is 800 pounds per square inch. The calculated z test statistic is a positive value that leads to a p-value of .045 for the test. If the significance level (α) for this test is .05, the null hypothesis would be rejected.

Question 13

Using the p-value rule for a population proportion or mean, if the level of significance is less than the p-value, the null hypothesis is rejected.

Question 14

Alpha (α) is the probability that the test statistic would assume a value at or more extreme than the observed value of the test.

Question 15

The null hypothesis is a statement that will be accepted only if there is convincing sample evidence that it is true.

Question 16

The level of significance, α, indicates the probability of rejecting a false null hypothesis.

Question 17

Everything else being constant, increasing the sample size decreases the probability of committing a Type II error.

Question 18

When the null hypothesis is true, there is no possibility of making a Type I error.

Question 19

When applying either the critical value rule or the p-value rule about a single mean, reducing the level of significance (α) will increase the size of the rejection region.

Question 20

When applying either the critical value rule or the p-value rule about a single mean, other relevant factors held constant, increasing the level of significance, α, from .05 to .10 will reduce the probability of a Type I error.

Question 21

It can be established at α = .05 that a majority of students favor the plus/minus grading system at a university if in a random sample of 500 students, 270 favor the system.

Question 22

We test H₀: μ ≤ 3.0; versus H_A: μ > 3.0. If = 3.44, s = .57, and n = 13, at a significance level of .05, we do not reject H₀. Assume that the population from which the sample is selected is normally distributed.

Question 23

We are testing H₀: μ = 32; versus H_A: μ > 32. If = 36, s = 1.6, and n = 30, at α = .05, we should reject H₀. Assume that the population from which the sample is selected is normally distributed.

Question 24

When we test H₀: p = .2; versus H_A: p ≠.2, with = .26 and n = 100, at alpha = .05, we reject the null hypothesis.

Question 25

The exact shape of the chi-square distribution depends on the degrees of freedom.

Question 26

We are testing H₀: μ ≥ 2.5; versus H_A: μ < 2.5. When = 2.46, s = .05, and n = 26, at α = .10 we reject the null hypothesis. Assume that the population from which the sample is selected is normally distributed.

Question 27

The chi-square distribution is a continuous probability distribution that is skewed to the left.

Question 28

We are testing H₀: μ ≤ .95; versus H_A: μ > .95. When = .99, s = .12, and n = 24, at alpha = .05, we reject H₀. Assume that the population from which the sample is selected is normally distributed.

Question 29

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes. The opinion poll recently sampled 1,500 voting age citizens. 1,020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66. Using the critical value rule, at α = .10, we would not reject H₀.

Question 30

Based on a random sample of 25 units of product X, the average weight is 102 lb and the sample standard deviation is 10 lb. We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lb. Assume the population is normally distributed. Therefore, the alternative hypothesis can be written as H_A: μ > 100.

Question 31

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes. The opinion poll recently sampled 1,500 voting age citizens. 1,020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66. Using the critical value rule, at α = .05, we would reject the null hypothesis.

Question 32

Based on a random sample of 25 units of product X, the average weight is 102 lb and the sample standard deviation is 10 lb. We would like to decide whether there is enough evidence to establish that the average weight for the population of product X is greater than 100 lb. Assume the population is normally distributed. Therefore, one way of expressing the null hypothesis is H₀: μ = 100.

Question 33

Based on a random sample of 25 units of product X, the average weight is 102 lb and the sample standard deviation is 10 lb. We would like to decide if there is enough evidence to establish that the average weight for the population of product X is greater than 100 lb. Assume the population is normally distributed. Using the critical value rule, at α = .05, we do not reject H₀.

Question 34

The power of a statistical test is the probability of rejecting the null hypothesis when it is false.

Question 35

Based on a random sample of 25 units of product X, the average weight is 102 lb and the sample standard deviation is 10 lb. We would like to decide whether there is enough evidence to establish that the average weight for the population of product X is greater than 100 lb. Assume the population is normally distributed. Using the critical value rule, at α = .01, we can reject the null hypothesis.

Question 36

We are testing H₀: p ≥ .7; versus H_A: p < .7. With = .63 and n = 100, at α = .01, we do not reject the null hypothesis.

Question 37

The HR department tested how long employees stay with the company in their current positions. A random sample of 50 employees yielded a mean of 2.79 years and σ = .76. The sample evidence indicates that the average time is less than 3 years and is significant at α = .01.

Question 38

After testing H₀: p = .33; versus H_A: p < .33; at α = .05, with = .20 and n = 100, we do not reject H₀.

Question 39

A microwave manufacturing company has just switched to a new automated production system. Unfortunately, the new machinery has been frequently failing and requiring repairs and service. Historically, the company has been able to provide its customers with a completion time of 6 days or less. To analyze whether the completion time has increased, the production manager took a sample of 36 jobs and found that the sample mean completion time was 6.5 days with a sample standard deviation of 1.5 days. At a significance level of .10 using the critical value rule, we can show that the completion time has increased.

Question 40

We are testing H₀: µ ≤ 42; versus H_A: µ > 42. When = 45, s = 1.2, and n = 15, at α = .01 we do not reject the null hypothesis. Assume that the population from which the sample is selected is normally distributed.

Question 41

As the Type II error, β, of a statistical test increases, the power of the test ________.

A) increases
B) decreases
C) stays the same
D) randomly fluctuates

Question 42

When testing a hypothesis about a single mean, if the sample size is 20, the population standard deviation is unknown, and the population is assumed to be a normal distribution, the correct test statistic to use is ________.

A) r
B) z
C) t
D) p-value

Question 43

χ²_α is the point on the vertical axis under the curve of the chi-square distribution that gives a right-hand tail area equal to α.

Question 44

When evaluating a new process, using the square root of the upper end of the confidence interval for σ² gives an estimate of the smallest that σ for the new process might reasonably be.

Question 45

The value of the test statistic is compared with a(n) ________ in order to decide whether the null hypothesis can be rejected.

A) α
B) β
C) p-value
D) critical value

Question 46

When testing a hypothesis about a single mean, a sample size of 200 is selected from a normally distributed population. If the population standard deviation is known, the correct test statistic to use is ________.

A) r
B) z
C) t
D) p-value

Question 47

The ________ hypothesis will be accepted only if there is convincing sample evidence that it is true.

A) z test
B) alternative
C) null
D) true

Question 48

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes. The opinion poll recently sampled 1,500 voting age citizens. 1,020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66. Identify the null hypothesis.

A) p ≠ .66
B) p > .66
C) p ≤ .66

Question 49

A null hypothesis is not rejected at a given level of significance. As the assumed value of the mean gets further away from the true population mean, the Type II error will ________.

A) increase
B) decrease
C) stay the same
D) randomly fluctuate

Question 50

Using a χ² test statistic to test the null hypothesis that the variance of a new process is equal to the variance of the current process and when applying the p-value rule, we are rejecting at a p-value less than α, we can conclude that the new process is more consistent than the current process.

Question 51

Assuming a fixed sample size, as α (Type I error) decreases, β (Type II error) ________.

A) increases
B) decreases
C) stays the same
D) randomly fluctuates

Question 52

Rejecting a true null hypothesis is called a ________ error.

A) Type I
B) Type II
C) Random
D) β

Question 53

A(n) ________ hypothesis is the statement that is being tested. It usually represents the status quo, and it is not rejected unless there is convincing sample evidence that it is false.

A) research
B) alternative
C) null
D) true

Question 54

In order to make statistical inferences about σ² that are valid using a chi-square distribution, the assumption is that the sampled population is also a chi-square distribution.

Question 55

For a fixed sample size, the lower we set α, the higher is the ________.

A) Type I error
B) Type II error
C) random error
D) p-value

Question 56

________ is not rejecting H₀ when H₀ is false.

A) A Type I error
B) A Type II error
C) The random error
D) α

Question 57

To compute a 95 percent confidence interval for σ², we use n − 1 degrees of freedom and the chi-square points on the distribution curve of χ²_α/2 and of χ²_1−(α/2).

Question 58

The ________ hypothesis is not rejected unless there is sufficient sample evidence to do so.

A) research
B) alternative
C) null
D) true

Question 59

Assuming that the null hypothesis is true, the ________ is the probability of observing a value of the test statistic that is at least as extreme as the value actually computed from the sample data.

A) α
B) β
C) p-value
D) Type I error

Question 60

When testing a hypothesis about a single mean, if the sample size is 51 and the population standard deviation is known, the correct test statistic to use is ________.

A) r
B) z
C) t
D) p-value

Question 61

In testing H₀: p = .2; versus H_A: p ≠ .2 using the critical value rule, with = .26 and n = 100, what is the value of the test statistic?

Question 62

In testing H₀: μ = 23; versus H_A: μ > 23 using the critical value rule, when = 26, s = 6, and n = 20, what is the value of the test statistic? Assume that the population from which the sample is selected is normally distributed.

Question 63

For a given hypothesis test, if we do not reject H₀, and H₀ is true,

A) no error has been committed.
B) a Type I error has been committed.
C) a Type II error has been committed.
D) a Type III error has been committed.

Question 64

When testing a null hypothesis about a single population mean and the population standard deviation is unknown, if the sample size is less than 30, one compares the computed test statistic for significance with a value from the ________ distribution.

A) t
B) z
C) binomial
D) hypergeometric

Question 65

In testing H₀: μ ≤ 23; versus H_A: μ > 23 using the critical value rule, when = 26, σ = 6, and n = 30, what is the value of the test statistic?

Question 66

Using either the critical value rule or the p-value rule, if a one-sided null hypothesis is rejected at a given significance level, then the corresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ________ be rejected at the same significance level.

A) always
B) sometimes
C) never

Question 67

Using the critical value rule, if a two-sided null hypothesis is rejected for a single mean at a given significance level, the corresponding one-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ________ be rejected at the same significance level.

A) always
B) sometimes
C) never

Question 68

Using the p-value rule, if a null hypothesis is rejected at a significance level of .01, it will ________ be rejected at a significance level of .05.

A) always
B) sometimes
C) never

Question 69

Using the p-value rule, if a null hypothesis is not rejected at a significance level of .05, it will ________ be rejected at a significance level of .01.

A) always
B) sometimes
C) never

Question 70

A recent study conducted by the state government attempts to determine whether the voting public supports a further increase in cigarette taxes. The opinion poll recently sampled 1,500 voting age citizens. 1,020 of the sampled citizens were in favor of an increase in cigarette taxes. The state government would like to decide if there is enough evidence to establish whether the proportion of citizens supporting an increase in cigarette taxes is significantly greater than .66. What is the alternative hypothesis?

A) p < .66
B) p > .66
C) p = .66
D) p ≤ .66

Question 71

Determine the p-value for H₀: p ≤ .5; versus H_A: p > .5, when n = 225 and = .54 (α = 0.05).

Question 72

Using the p-value rule, if a null hypothesis is rejected at a significance level of .05, it will ________ be rejected at a significance level of .01.

A) always
B) sometimes
C) never

Question 73

Using either the critical value rule or the p-value rule, if a one-sided null hypothesis for a single mean cannot be rejected at a given significance level, then the corresponding two-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ________ be rejected at the same significance level.

A) always
B) sometimes
C) never

Question 74

For the following hypothesis test, where H₀: μ ≤ 10; vs. H_A: μ > 10, we reject H₀ at level of significance α and conclude that the true mean is greater than 10, when the true mean is really 8. Based on this information, we can state that we have

A) made a Type I error.
B) made a Type II error.
C) made the correct decision.
D) increased the power of the test.

Question 75

To apply the p-value rule, determine the p-value for H₀: p = .5; versus H_A: p ≠.5, when n = 225 and = .54 (α = .05).

Question 76

When computing a 95 percent confidence interval for σ² with a sample of n = 30, what values of χ² would we use in the calculations?

A) 45.7222 and 16.0471
B) 46.9792 and 16.7908
C) 42.5569 and 17.7083
D) 43.7729 and 18.4926

Question 77

Using the critical value rule, if a two-sided null hypothesis cannot be rejected for a single mean at a given significance level, then the corresponding one-sided null hypothesis (i.e., the same sample size, the same standard deviation, and the same mean) will ________ be rejected at the same significance level.

A) always
B) sometimes
C) never

Question 78

For the following hypothesis test, where H₀: μ ≤ 10; vs. H_A: μ > 10, we reject H₀ at level of significance α and conclude that the true mean is greater than 10, when the true mean is really 14. Based on this information, we can state that we have

A) made a Type I error.
B) made a Type II error.
C) made the correct decision.
D) increased the power of the test.

Question 79

The value of χ²_α in a particular situation depends on

A) the left-hand tail area α.
B) the number of degrees of freedom.
C) the right-hand tail area α.
D) the left-hand tail area α and the number of degrees of freedom.
E) the number of degrees of freedom and the right-hand tail area α.

Question 80

A Type II error is defined as ________ H₀, when it should ________.

A) failing to reject, be rejected
B) failing to reject, not be rejected
C) rejecting, not be rejected
D) rejecting, be rejected