ST 560 Module 9

For the case where σ is unknown, the test statistic has a t distribution. How many degrees of freedom does it have? a.n - 1 b.5 c.30 d.n

a.n - 1

Which of the following describe a Type II Error? a.Accept H₀ when H₀ is false. b.Reject H₀ when H₀ is true. c.Accept H₀ when H₀ is true. d.Reject H₀ when H₀ is false.

a.Accept H₀ when H₀ is false.

A fast food restaurant has automatic drink dispensers to help fill orders more quickly. When the 12 ounce button is pressed, they would like for exactly 12 ounces of beverage to be dispensed. There is, however, undoubtedly some variation in this amount. The company does not want the machine to systematically over fill or under fill the cups. Which of the following gives the correct set of hypotheses? a.H₀: µ = 12, Hα: µ ≠ 12 b.H₀: µ ≤ 12, Hα: µ > 12 c.H₀: µ ≥ 12, Hα: µ < 12 d.H₀: µ > 12, Hα: µ < 12

a.H₀: µ = 12, Hα: µ ≠ 12

The average gasoline price of one of the major oil companies has been hovering around $2.20 per gallon. Because of cost reduction measures, it is announced that there will be a significant reduction in the average price over the next month. In order to test this belief, we wait one month, then randomly select a sample of 36 of the company's gas stations. We find that the average price for the stations in the sample was $2.15. The standard deviation of the prices for the selected gas stations is $0.10. Given that the p-value is 0.002, state the conclusion. Use α = 0.01. a.The p-value is less than α = 0.01, so we can reject H0. b.The p-value is greater than α = 0.01, so we cannot reject H0. c.The p-value is less than α = 0.01, so we cannot reject H0. d.The p-value is greater than α = 0.01, so we can reject H0.

a.The p-value is less than α = 0.01, so we can reject H0.

The level of significance specified by the user determines the probability of making a a.Type I error. b.Type II error. c.random sampling error. d.normal probability error.

a.Type I error.

What type of error occurs if you fail to reject H₀ when, in fact, it is not true? a.Type II b.Type I c.either Type I or Type II, depending on the level of significance d.either Type I or Type II, depending on whether the test is one tail or two tail

a.Type II

A student wants to determine if pennies are really fair, meaning equally likely to land heads up or tails up. He flips a random sample of 50 pennies and finds that 28 of them land heads up. Calculate the p-value and state the conclusion. Use α = 0.05. a.p-value = 0.396. Do not reject H₀. b.p-value = 0.198. Reject H₀. c.p-value = 0.396. Reject H₀. d.p-value = 0.198. Do not reject H₀.

a.p-value = 0.396. Do not reject H₀. (P-value is based upon a standard normal distribution. When looking up the test statistic (z = 0.85), remember that the value found must be doubled because this is a two-sided test.)

When the null hypothesis is rejected, it is a.possible a Type I error has occurred. b.not possible a Type I error has occurred. c.possible a Type II error has occurred. d.possible either a Type I or Type II error has occurred.

a.possible a Type I error has occurred.

When conducting a test of significance, it is recommended to either a.reject H₀ or do not reject H₀. b.reject H₀ or reject Ha. c.reject Ha or do not reject Ha. d.accept H₀ or accept Ha.

a.reject H₀ or do not reject H₀.

For the case where σ is unknown, what statistic is used to estimate σ? a.s b.p̄ c.n d.x̄

a.s

In hypothesis testing, the tentative assumption about the population parameter is called a.the null hypothesis. b.the hypothesis test. c.the research hypothesis. d.the alternative hypothesis.

a.the null hypothesis.

For a two-tail test, the p-value is the probability of obtaining a value for the test statistic as a.unlikely as that provided by the sample. b.likely as that provided by the population. c.unlikely as that provided by the population. d.likely as that provided by the sample.

a.unlikely as that provided by the sample.

What is the probability of making a Type I error? a.α b.0.01 c.0.05 d.σ

a.α

The average gasoline price of one of the major oil companies has been hovering around $2.20 per gallon. Because of cost reduction measures, it is announced that there will be a significant reduction in the average price over the next month. In order to test this belief, we wait one month, then randomly select a sample of 36 of the company's gas stations. We find that the average price for the stations in the sample was $2.15. The standard deviation of the prices for the selected gas stations is $0.10. State the appropriate null and alternative hypothesis for testing the company's claim. a. H₀: x̄ ≤ $2.15, Hα: x̄ > $2.15 b. H₀: µ ≥ $2.20, Hα: µ < $2.20 c. H₀: µ ≤ $2.20, Hα: µ > $2.20 d. H₀: x̄ ≥ $2.15, Hα: x̄ < $2.15

b. H₀: µ ≥ $2.20, Hα: µ < $2.20

A student wants to determine if pennies are really fair, meaning equally likely to land heads up or tails up. He flips a random sample of 50 pennies and finds that 28 of them land heads up. What are the appropriate null and alternative hypotheses? a.H₀: p ≤ 0.5, Hα: p > 0.5 b.H₀: p = 0.5, Hα: p ≠ 0.5 c.H₀: p ≥ 28, Hα: p < 28 d.H₀: p ≥ 0.5, Hα: p < 0.5

b.H₀: p = 0.5, Hα: p ≠ 0.5

The average hourly wage of computer programmers with 2 years of experience has been $21.80. Because of high demand for computer programmers, it is believed there has been a significant increase in the average wage of computer programmers. To test whether or not there has been an increase, the correct hypotheses to be tested are a.H₀: µ = 21.80, Hα: µ ≠ 21.80 b.H₀: µ ≤ 21.80, Hα: µ > 21.80 c.H₀: µ ≥ 21.80, Hα: µ < 21.80 d.H₀: µ > 21.80, Hα: µ < 21.80

b.H₀: µ ≤ 21.80, Hα: µ > 21.80

Which of the following describe a Type I Error? a.Accept H₀ when H₀ is false. b.Reject H₀ when H₀ is true. c.Accept H₀ when H₀ is true. d.Reject H₀ when H₀ is false.

b.Reject H₀ when H₀ is true.

By controlling the sample size, the user can control the probability of making a a.Type I error. b.Type II error. c.random sampling error. d.normal probability error.

b.Type II error.

Smaller values of α have the disadvantage of increasing the probability of making a a.Type I error. b.Type II error. c.random sampling error. d.normal probability error.

b.Type II error.

Whenever the probability of making a Type II error has not been determined and controlled, only two conclusions are possible. We either reject H₀ or a.reject Ha. b.do not reject H₀ . c.do not reject Ha. d.accept H₀ .

b.do not reject H₀ .

For a given sample size, a.decreasing α will decrease β. b.increasing α will decrease β. c.decreasing α will not affect β. d.increasing α will not affect β.

b.increasing α will decrease β.

The normal probability distribution can be used to approximate the sampling distribution of p as long as a.n ≥ 30. b.np ≥ 5 and n(1 − p) ≥ 5. c.np ≥ 30 and n(1 − p) ≥ 30. d.n ≥ 5.

b.np ≥ 5 and n(1 − p) ≥ 5.

When the null hypothesis is not rejected, it is a.possible a Type I error has occurred. b.possible a Type II error has occurred. c.not possible a Type II error has occurred. d.possible either a Type I or Type II error has occurred.

b.possible a Type II error has occurred.

Which of the following does not need to be known in order to compute the p-value? a.the value of the test statistic b.the level of significance c.the distribution of the data d.knowledge of whether the test is one-tailed or two-tailed

b.the level of significance

In hypothesis testing, a.the smaller the Type I error, the smaller the Type II error will be. b.the smaller the Type I error, the larger the Type II error will be. c.Type II error will not be effected by Type I error. d.the sum of Type I and Type II errors must equal to 1.

b.the smaller the Type I error, the larger the Type II error will be.

A student believes that no more than 20% of the students who finish a statistics course get an A. A random sample of 100 students was taken. Twenty-two percent of the students in the sample received A's. Calculate the test statistic. a.t = - 0.5 b.z = 0.5 c.t = 0.5 d.z = - 0.5

b.z = 0.5

A student wants to determine if pennies are really fair, meaning equally likely to land heads up or tails up. He flips a random sample of 50 pennies and finds that 28 of them land heads up. What is the value of the test statistic? a.z = 0.56 b.z = 0.85 c.z = 1.5 d.z = 0.5

b.z = 0.85 z = (p^ - p) / sqrt( p * (p-1) / n) z = (.56 - .50) / sqrt( .5*.5)/50) z = 0.06/sqrt(.25/50) = 0.85

Which of the following null hypotheses cannot be correct? a. H₀: µ ≥ 10 b. H₀: µ = 10 c. H₀: µ ≠ 10 d. H₀: µ ≤ 10

c. H₀: µ ≠ 10

The average gasoline price of one of the major oil companies has been hovering around $2.20 per gallon. Because of cost reduction measures, it is announced that there will be a significant reduction in the average price over the next month. In order to test this belief, we wait one month, then randomly select a sample of 36 of the company's gas stations. We find that the average price for the stations in the sample was $2.15. The standard deviation of the prices for the selected gas stations is $0.10. Determine the test statistic. a. z = (2.15-2.20) / (0.10/√36) b. t = (2.20-2.15) / (0.10/√36) c. t = (2.15-2.20) / (0.10/√36) d. z = (2.20-2.15) / (0.10/√36)

c. t = (2.15-2.20) / (0.10/√36)

A news reporter states that the average number of temperature in January has never dropped below 10 degrees Fahrenheit. You go online to research this claim. The appropriate hypotheses are a.H₀: µ = 10, Hα: µ ≠ 10 b.H₀: µ ≤ 10, Hα: µ > 10 c.H₀: µ ≥ 10, Hα: µ < 10 d.H₀: µ > 10, Hα: µ < 10

c.H₀: µ ≥ 10, Hα: µ < 10

The average number of hours for a random sample of mail order pharmacists from company A was 50.1 hours last year. It is believed that changes to medical insurance have led to a reduction in the average work week. To test the validity of this belief, the hypotheses are a.H₀: µ = 50.1, Hα: µ ≠ 50.1 b.H₀: µ ≤ 50.1, Hα: µ > 50.1 c.H₀: µ ≥ 50.1, Hα: µ < 50.1 d.H₀: µ > 50.1, Hα: µ < 50.1

c.H₀: µ ≥ 50.1, Hα: µ < 50.1

If both the Type I and Type II error probabilities have been controlled at allowable levels then the conclusion based off of the hypothesis test should be to either a.Reject H₀ or do not reject H₀. b.Reject Ha or do not reject Ha. c.Reject H₀ or accept H₀. d.Reject Ha or accept Ha.

c.Reject H₀ or accept H₀.

When carrying out a test of significance, what type of error do we control? a.random sampling error b.nonresponse error c.Type I error d.Type II error

c.Type I error

The p-value a.can be any positive value. b.can be any value, negative or positive. c.must be a number between zero and 1. d.can be any value.

c.must be a number between zero and 1.

Applications of hypothesis testing that only control for the Type I error are called a.research tests. b.assumption calculations. c.significance tests. d.levels of significance.

c.significance tests.

It has been stated that at least 75 out of every 100 people who go to the movies on Saturday night buy popcorn. Identify the null and alternative hypothesis. a.H₀: p ≤ 0.75, Hα: p > 0.75 b.H₀: μ ≥ 0.75, Hα: μ < 0.75 c.H₀: μ ≤ 0.75, Hα: μ > 0.75 d.H₀: p ≥ 0.75, Hα: p < 0.75

d.H₀: p ≥ 0.75, Hα: p < 0.75

A sample of 30 cookies is taken to test the claim that each cookie contains at least 9 chocolate chips. The average number of chocolate chips per cookie in the sample was 7.8 with a standard deviation of 3. Is it possible to commit a Type II error in this situation? If it is, compute the probability of a Type II error if the true number of chocolate chips per cookie is 8. If it is not, then state why it is not possible. a.Yes. P(Type II error) = 0.24 b.Yes. P(Type II error) = 0.33 c.Yes. P(Type II error) = 0.43 d.No. The null hypothesis would not be rejected, so it is not possible to make a Type II error.

d.No. The null hypothesis would not be rejected, so it is not possible to make a Type II error.

In decision-making situations, it is recommended that the hypothesis testing procedure be extended to control the probability of making a a.random sampling error. b.nonresponse error. c.Type I error. d.Type II error.

d.Type II error.

For a lower tail test, the p-value is the probability of obtaining a value for the test statistic a.at least as large as that provided by the sample. b.at least as small as that provided by the population. c.at least as large as that provided by the population. d.at least as small as that provided by the sample.

d.at least as small as that provided by the sample.

As the test statistic becomes larger, the p-value a.becomes larger. b.stays the same, since the sample size has not been changed. c.becomes negative. d.becomes smaller.

d.becomes smaller.

The power curve provides the probability of a.correctly accepting the null hypothesis. b.incorrectly accepting the null hypothesis. c.incorrectly accepting the null hypothesis. d.correctly rejecting the null hypothesis.

d.correctly rejecting the null hypothesis.

The probability of making a Type I error when the null hypothesis is true as an equality is called the a.possibility of error. b.null hypothesis. c.alternative hypothesis. d.level of significance.

d.level of significance.

The p-value is a probability that measures the support (or lack of support) for the a.alternative hypothesis. b.population. c.sample statistic. d.null hypothesis.

d.null hypothesis.

The average gasoline price of one of the major oil companies has been hovering around $2.20 per gallon. Because of cost reduction measures, it is announced that there will be a significant reduction in the average price over the next month. In order to test this belief, we wait one month, then randomly select a sample of 36 of the company's gas stations. We find that the average price for the stations in the sample was $2.15. The standard deviation of the prices for the selected gas stations is $0.10. Given that the test statistic for this sample is t = -3, determine the p-value. a.p-value = 0.004 b.p-value = 0.2 c.p-value = 0.4 d.p-value = 0.002

d.p-value = 0.002 (From a t-distribution table, we determine that the p-value is between 0.001 and 0.0025)

For a given level of significance, increasing the sample size will a.increase the likelihood of making a Type I error. b.increase the standard deviation of the sampling distribution. c.reduce the power of the test. d.reduce β.

d.reduce β.