Question 1

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: = 52, S = 22. Suppose the alternative you wanted to test was H₁: μ < 60. State the correct rejection region for α = 0.05. A) Reject H₀ if t > 1.6604. B) Reject H₀ if t < -1.6604. C) Reject H₀ if t > 1.9842 or Z < -1.9842. D) Reject H₀ if t < -1.9842.

Accepted Answer

Since the alternative hypothesis is one-tailed (μ < 60), we need to use a one-tailed t-test. With a sample size of 100, the degrees of freedom (df) are 99. Using a t-distribution table with α = 0.05 and df = 99, the critical t-value is -1.6604. Therefore, we reject the null hypothesis if our calculated t-value is less than -1.6604. This means our rejection region is t < -1.6604. Thus, the correct answer is B.

Question 2

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold:  = 52, S = 22. Give the null and alternative hypotheses to determine if the number of tissues used during a cold is less than 60.
A) H₀: μ ≤ 60 and H₁: μ > 60.
B) H₀: μ ≥ 60 and H₁: μ < 60.
C) H₀:  ≥ 60 and H₁:  < 60.
D) H₀:  = 52 and H₁:  ≠ 52.

Accepted Answer

The null hypothesis should be that the mean number of tissues used during a cold is greater than or equal to 60 (H₀: μ ≥ 60) and the alternative hypothesis should be that the mean number of tissues used during a cold is less than 60 (H₁: μ < 60). This is because we are testing if there is evidence to suggest that the true mean number of tissues used during a cold is less than the traditionally packaged amount of 60 tissues. Choice A is incorrect because the alternative hypothesis should be that the mean number of tissues used during a cold is less than 60, not greater than. Choice C is incorrect because it states the null and alternative hypothesis in terms of the sample data, rather than the population parameters. Choice D is irrelevant to the stated problem.

Question 3

The symbol for the power of a statistical test is
A) α.
B) 1 - α.
C) β.
D) 1 - β.

Accepted Answer

The answer of The symbol for the power of a...

Question 4

You have created a 95% confidence interval for μ with the result 10 ≤ μ ≤ 15. What decision will you make if you test H₀: μ =16 versus H₁: μ ≠ 16 at α = 0.05?
A) Reject H₀ in favor of H₁.
B) Do not reject H₀ in favor of H₁.
C) Fail to reject H₀ in favor of H₁.
D) We cannot tell what our decision will be from the information given.

Accepted Answer

The answer of You have created a 95% confidence interval...

Question 5

The value that separates a rejection region from a non-rejection region is called the ________.

Accepted Answer

The answer of The value that separates a rejection region...

Question 6

If, as a result of a hypothesis test, you reject the null hypothesis when it is false, then you have committed
A) a Type II error.
B) a Type I error.
C) no error.
D) an acceptance error.

Accepted Answer

Rejecting the null hypothesis when it is false means you have made the correct decision, hence no error has been committed.

Question 7

The symbol for the probability of committing a Type II error of a statistical test is
A) α.
B) 1 - α.
C) β.
D) 1 - β.

Accepted Answer

The symbol for the probability of committing a Type II error of a statistical test is β. Option A represents the symbol for the probability of committing a Type I error, while option B represents the complement of the Type I error rate. Option D represents the complement of the Type II error rate.

Question 8

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold:  = 52, S = 22. Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following decisions is correct?
A) At α = 0.05, you do not reject H₀.
B) At α = 0.05, you reject H₀.
C) At α = 0.10 you reject H₀.
D) At α = 0.10, you do not reject H₀.

Accepted Answer

We can use a one-sample t-test to test the hypothesis:

H₀: μ = 60 (the true mean of tissues per cold is 60)
H₁: μ < 60 (the true mean of tissues per cold is less than 60)

The test statistic is calculated as:

t = (x̄ - μ) / (s / sqrt(n)) = (52 - 60) / (22 / sqrt(100)) = -3.64

Using a t-table with 99 degrees of freedom (n-1), at a significance level of α = 0.05 and a one-tailed test, the critical value is -1.660. Since our test statistic is smaller than the critical value, we reject the null hypothesis.

Therefore, the correct decision is to reject H₀ at α = 0.05, which is option B. We have evidence to suggest that the true mean number of tissues used during a cold is less than 60.

Question 9

It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if
A) a two-tail test for μ is used.
B) a one-tail test for μ is used.
C) Both of the previous statements are true.
D) None of the previous statements is true.

Accepted Answer

The answer of It is possible to directly compare the...

Question 10

The symbol for the probability of committing a Type I error of a statistical test is
A) α.
B) 1 - α.
C) β.
D) 1 - β.

Accepted Answer

The symbol for the probability of committing a Type I error of a statistical test is α.

Question 11

Suppose we wish to test H₀: μ ≤ 47 versus H₁: μ > 47. What will result if we conclude that the mean is greater than 47 when its true value is really 52?
A) We have made a Type I error.
B) We have made a Type II error.
C) We have made a correct decision.
D) None of the above are correct.

Accepted Answer

We have made a correct decision because the true mean (52) is indeed greater than 47, which aligns with the alternative hypothesis H₁: μ > 47.

Question 12

The symbol for the confidence coefficient of a statistical test is
A) α.
B) 1 - α.
C) β.
D) 1 - β.

Accepted Answer

The confidence coefficient is the probability that the true population parameter is within the confidence interval. It is represented by the symbol 1 - α, where α is the significance level.

Question 13

The symbol for the level of significance of a statistical test is
A) α.
B) 1 - α.
C) β.
D) 1 - β.

Accepted Answer

The symbol for the level of significance of a statistical test is α. This represents the probability of rejecting the null hypothesis when it is actually true. The level of significance is typically set at 0.05, meaning that there is a 5% chance of rejecting the null hypothesis when it is true.

Question 14

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold:  = 52, S = 22. Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following conclusions is correct?
A) At α = 0.05, there is not sufficient evidence to conclude that the mean number of tissues used during a cold is 60 tissues.
B) At α = 0.05, there is sufficient evidence to conclude that the mean number of tissues used during a cold is 60 tissues.
C) At α = 0.05, there is insufficient evidence to conclude that the mean number of tissues used during a cold is not 60 tissues.
D) At α = 0.10, there is sufficient evidence to conclude that the mean number of tissues used during a cold is not 60 tissues.

Accepted Answer

The answer of How many tissues should the Kimberly Clark...

Question 15

You have created a 95% confidence interval for μ with the result 10 ≤ μ ≤ 15. What decision will you make if we test H₀: μ =16 versus H₁: μ ≠ 16 at α = 0.10?
A) Reject H₀ in favor of H₁.
B) Do not reject H₀ in favor of H₁.
C) Fail to reject H₀ in favor of H₁.
D) We cannot tell what our decision will be from the information given.

Accepted Answer

A) The 90% confidence interval is narrower than (10, 15), which still does not contain 16.

Question 16

The power of a statistical test is
A) the probability of not rejecting H₀ when it is false.
B) the probability of rejecting H₀ when it is true.
C) the probability of not rejecting H₀ when it is true.
D) the probability of rejecting H₀ when it is false.

Accepted Answer

The answer of The power of a statistical test is
A)...

Question 17

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold:  = 52, S = 22. Using the sample information provided, calculate the value of the test statistic.
A) t = (52 - 60) / 22
B) t = (52 - 60) / (22/100)
C) t = (52 - 60) / (22/100²)
D) t = (52 - 60) / (22/10)

Accepted Answer

The answer of How many tissues should the Kimberly Clark...

Question 18

You have created a 95% confidence interval for μ with the result 10 ≤ μ ≤ 15. What decision will you make if we test H₀: μ =16 versus H₁: μ ≠ 16 at α = 0.01?
A) Reject Ho in favor of H₁.
B) Do not reject Ho in favor of H₁.
C) Fail to reject Ho in favor of H₁.
D) You cannot tell what our decision will be from the information given.

Accepted Answer

D) The 99% confidence interval is wider than (10, 15), which could have contained 16 or not have contained 16.

Question 19

Suppose you want to test H₀: μ ≥ 30 versus H₁: μ < 30. Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H₀ in favor of H₁?
A)  = 28, S = 6
B)  = 27, S = 4
C)  = 32, S = 2
D)  = 26, S = 9

Accepted Answer

We need a sample result that is farthest away from the null hypothesis value of μ=30. The sample mean in choice B is only 3 units away from the null hypothesis value whereas the sample means in choices A, C, and D are closer to the null hypothesis value. Additionally, the sample standard deviation in choice B is smaller than the other options which indicates less variability in the data and thus a stronger result in favor of rejecting H₀.

Question 20

Which of the following statements is NOT true about the level of significance in a hypothesis test?
A) The larger the level of significance, the more likely you are to reject the null hypothesis.
B) The level of significance is the maximum risk we are willing to accept in making a Type I error.
C) The significance level is also called the α level.
D) The significance level is another name for Type II error.

Accepted Answer

The significance level is not another name for Type II error. Type II error is the error made when we fail to reject a false null hypothesis. The significance level only pertains to Type I error, which is the error made when we reject a true null hypothesis.

Quiz 9: Fundamentals of Hypothesis Testing: One-Sample Tests

The symbol for the power of a statistical test is

You have created a 95% confidence interval for μ with the result 10 ≤ μ ≤ 15. What decision will you make if you test H₀: μ =16 versus H₁: μ ≠ 16 at α = 0.05?

The value that separates a rejection region from a non-rejection region is called the ________.

If, as a result of a hypothesis test, you reject the null hypothesis when it is false, then you have committed

The symbol for the probability of committing a Type II error of a statistical test is

It is possible to directly compare the results of a confidence interval estimate to the results obtained by testing a null hypothesis if

The symbol for the probability of committing a Type I error of a statistical test is

Suppose we wish to test H₀: μ ≤ 47 versus H₁: μ > 47. What will result if we conclude that the mean is greater than 47 when its true value is really 52?

The symbol for the confidence coefficient of a statistical test is

The symbol for the level of significance of a statistical test is

You have created a 95% confidence interval for μ with the result 10 ≤ μ ≤ 15. What decision will you make if we test H₀: μ =16 versus H₁: μ ≠ 16 at α = 0.10?

The power of a statistical test is

You have created a 95% confidence interval for μ with the result 10 ≤ μ ≤ 15. What decision will you make if we test H₀: μ =16 versus H₁: μ ≠ 16 at α = 0.01?

Suppose you want to test H₀: μ ≥ 30 versus H₁: μ < 30. Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H₀ in favor of H₁?

Which of the following statements is NOT true about the level of significance in a hypothesis test?