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: X = 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

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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: X = 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: X ≥ 60 and H₁: X < 60.
D) H₀: X = 52 and H₁: X ≠ 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 is less than 60, as we are testing whether the number of tissues used is less than the reported mean of 60. Thus, option B is the correct choice. Option A is incorrect because it assumes that the mean is already less than 60. Option C is incorrect because it uses the sample mean, rather than the population mean, as the statistic of interest. Option D is incorrect because it is testing whether the sample mean is different from 52, rather than testing whether the population mean is less than 60.

Question 3

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 H₀ in favor of H₁.
B) Do not reject H₀ in favor of H₁.
C) Fail to reject H₀ in 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 4

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. If she wants to have a level of significance at 0.01, what rejection region should she use? A) Reject H₀ if t < -2.3263. B) Reject H₀ if t < -2.5758. C) Reject H₀ if t > 2.3263. D) Reject H₀ if t > 2.5758.

Accepted Answer

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Question 5

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) X = 28, S = 6
B) X = 27, S = 4
C) X = 32, S = 2
D) X = 26, S = 9

Accepted Answer

The answer of Suppose you want to test H₀: μ...

Question 6

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 7

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are: A) H₀: μ ≥ 30 versus H₁: μ < 30. B) H₀: μ ≤ 30 versus H₁: μ > 30. C) H₀: X ≥ 30 versus H₁: X < 30. D) H₀: X ≤ 30 versus H₁: X > 30.

Accepted Answer

The appropriate hypothesis to test in this scenario is if the mean age of the customers is greater than 30, which is a one-tailed test. Therefore, the null hypothesis (H₀) will state the opposite, that the mean age is less than or equal to 30. The alternative hypothesis (H₁) will state that the mean age is greater than 30. 
H₀: μ ≤ 30
H₁: μ > 30

Option A is incorrect because the null hypothesis states that the mean age is greater than or equal to 30, which is not the alternative hypothesis.
Option C is incorrect because it uses X as the variable, which refers to a sample mean, but the hypotheses should be about the population mean μ. 
Option D is also incorrect for the same reason as option C.

Question 8

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

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Question 9

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 is correct.

Accepted Answer

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Question 10

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to have a level of significance at 0.01, what decision should she make?
A) Reject H₀.
B) Reject H₁.
C) Do not reject H₀.
D) We cannot tell what her decision should be from the information given.

Accepted Answer

We need to perform a one-sample t-test to test the hypothesis. The null hypothesis (H₀) is that the mean age of the customers is less than or equal to 30, and the alternative hypothesis (H₁) is that the mean age is greater than 30. We can set the level of significance at 0.01, which means that we allow a maximum of 1% chance of making a Type I error.

The test statistic is calculated as:

t = (sample mean - hypothesized mean)/(sample standard deviation/sqrt(sample size))

Plugging in the values, we get:

t = (30.45 - 30)/(5/sqrt(250)) = 2.06

The degrees of freedom for the t-distribution is 249 (sample size - 1).

Using a t-table or a calculator, we can find the critical value of t at 0.01 significance level and 249 degrees of freedom to be 2.330.

Since 2.06 < 2.330, we fail to reject the null hypothesis. Therefore, we can conclude that there is not enough evidence to suggest that the mean age of the customers is greater than 30. The owner should not alter the entertainment to appeal to an older crowd.

Question 11

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 rejecting the null hypothesis when it is true (Type I error), while Type II error is the probability of accepting the null hypothesis when it is false.

Question 12

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: X = 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 μ < 60, this is a one-tailed test to the left. Using a t-distribution with 99 degrees of freedom (n-1), and a significance level of 0.05, we need to find the t-value that corresponds to a 0.05 area to the left of it. Using a t-table, we find that the t-value is -1.6604. Therefore, we reject the null hypothesis if the calculated t-value is less than -1.6604. Thus, the correct rejection region is t < -1.6604, which is option B.

Question 13

A ________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.
A) significance level
B) critical value
C) test statistic
D) parameter

Accepted Answer

A test statistic is a numerical quantity calculated from data in a sample that is used to determine whether to reject the null hypothesis. It is compared to a critical value, which is determined by the significance level, in order to make the decision. A parameter is a numerical value that represents a characteristic of a population, whereas a test statistic is computed from a sample.

Question 14

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

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

Question 15

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 16

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 17

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 18

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 19

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: X = 52, S = 22. Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following decision 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 can use a one-sample t-test to determine whether the sample mean (52) is significantly different from the population mean (60) at a 0.05 level of significance. The test statistic is calculated as follows:

t = (52 - 60) / (22 / sqrt(100)) = -4

Using a t-distribution table with 99 degrees of freedom (n-1), the critical value for a two-tailed test at a 0.05 level of significance is ±1.984. Since our test statistic (-4) falls in the rejection region (t < -1.984 or t > 1.984), we reject the null hypothesis and conclude that there is sufficient evidence to suggest that the true mean number of tissues used during a cold is less than 60. Therefore, the correct decision is B: At α = 0.05, you reject H₀.

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: X = 52, S = 22. Suppose the test statistic does fall in the rejection region at α = 0.05. Which of the following conclusion 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...

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

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?

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?

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

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?

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

A ________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.

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

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 power of a statistical test is

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