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 we are testing whether the population mean is less than 60, this is a one-tailed test. Using a t-test with a sample size of 100 and a significance level of 0.05, the rejection region for the null hypothesis (μ = 60) is t < -1.6604 or t > 1.6604. Since our alternative hypothesis states that μ < 60, we only need to consider the left tail of the distribution. Therefore, we reject the null hypothesis if t < -1.6604, which is the correct rejection region.

Question 2

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 is β. Therefore, option C is the correct choice. Option A is incorrect because S1, U1, and B1 are not symbols used in probability notation. Option B is incorrect because it represents the probability of correctly rejecting a false null hypothesis (Type I error) rather than the probability of committing a Type II error. Option D is incorrect because it represents the probability of correctly accepting a true null hypothesis rather than the probability of committing a Type II error.

Question 3

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, and it is represented by _α_. in choice A. The other options (B, C, and D) represent other concepts in hypothesis testing (type I error, type II error, and power, respectively).

Question 4

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 represented by α. Option A mentions α in its answer choice.

Question 5

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 6

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 7

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 usually represented by 1 - α, where α is the level of significance or the probability of rejecting the null hypothesis when it is actually true. Therefore, option B is the correct answer. Option A is not a standard symbol for the confidence coefficient. Options C and D represent the probability of making a type II error or accepting the null hypothesis when it is actually false, which is different from the confidence coefficient.

Question 8

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 9

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 H₀in favor of H₁. B)Do not reject H₀in favor of H₁. C)Fail to reject H₀in favor of H₁. D)We cannot tell what our decision will be from the information given.

Accepted Answer

Since the null hypothesis H₀: μ = 16 falls outside of the confidence interval of 10 ≤ μ ≤ 15, we can reject it in favor of the alternative hypothesis H₁: μ ≠ 16. Furthermore, since the significance level is at α = 0.05, we can infer that we have sufficient evidence to reject the null hypothesis. Therefore, we choose option A.

Question 10

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 H₀in favor of H₁. B)Do not reject H₀in favor of H₁. C)Fail to reject H₀in favor of H₁. D)You cannot tell what our decision will be from the information given.

Accepted Answer

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

Question 11

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: ≠ 52. D)H₀: = 52 and H₁: ≠ 52.

Accepted Answer

The null hypothesis should state that the mean number of tissues used during a cold is greater than or equal to 60, while the alternative hypothesis should state that the mean number of tissues used during a cold is less than 60. This is because we are testing whether there is evidence to support the claim that the mean number of tissues used during a cold is less than the reported mean of 60. Therefore, the correct null and alternative hypotheses are: H₀ : μ ≥ 60 and H₁: μ < 60.

Question 12

Suppose you want to test H₀: μ ≥ 30 versus H₁ : μ < 30.Which of the following possible sample results based on a sample size of 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 to test whether μ is less than 30. Therefore, we are interested in the lower tail of the t-distribution. A smaller value of t indicates that the sample mean is farther away from 30. Among the given options, option B has the smallest sample mean and smallest standard deviation, which corresponds to the largest t-value. Therefore, option B gives the strongest evidence to reject H₀ in favor of H₁.

Question 13

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 H₀in favor of H₁. B)Do not reject H₀in favor of H₁. C)Fail to reject H₀in favor of H₁. D)We cannot tell what our decision will be from the information given.

Accepted Answer

The 95% confidence interval does not include 16, suggesting that 16 is not a plausible value for μ, leading to the rejection of H₀ at α = 0.10.

Question 14

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

Accepted Answer

The symbol for the power of a statistical test is β, therefore the best choice is D.

Question 15

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 16

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 do not reject H₀. D)At α = 0.10,you reject H₀.

Accepted Answer

We will use a one-tailed t-test with the following hypotheses: H0: μ = 60 (the mean number of tissues used during a cold is 60) Ha: μ < 60 (the mean number of tissues used during a cold is less than 60) The sample size is large (n = 100) and the population standard deviation is unknown, so we will use a t-test. The test statistic is: t = (x̄ - μ) / (s / √n) = (52 - 60) / (22 / √100) = -36 / 22 = -1.64 The degrees of freedom are n - 1 = 99, and the critical t-value for α = 0.05 and a one-tailed test is t = -1.66. Since our calculated t-value (-1.64) falls in the rejection region (t < -1.66), we reject the null hypothesis and conclude that the mean number of tissues used during a cold is less than 60. Therefore, the correct decision is to reject H₀, which is choice B.

Question 17

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 is greater than 47.

Question 18

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 power of a statistical test is the probability of correctly rejecting the null hypothesis (H0) when it is false.

Question 19

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 statement "The significance level is another name for Type II error" is not true. The significance level is the probability of making a Type I error, whereas the Type II error is the probability of failing to reject a false null hypothesis.

Question 20

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...

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

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

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

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

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

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?

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 size of 36 gives the strongest evidence to reject H0 in favor of H1?

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 symbol for the power of a statistical test is

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

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 power of a statistical test is

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

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?

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 size of 36 gives the strongest evidence to reject H₀ in favor of H₁?

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?

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?