Question 1

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

The answer of Suppose we wish to test H₀: μ...

Question 2

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 3

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

Accepted Answer

The answer of If,as a result of a hypothesis test,you...

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

The answer of The owner of a local nightclub has...

Question 5

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 left-tailed (H₁: μ < 60), we need to reject the null hypothesis (H₀: μ = 60) when the sample mean is significantly smaller than 60. The rejection region for α = 0.05 is obtained from a t-distribution with 100-1=99 degrees of freedom:

t < -t(0.05, 99) = -1.6604

Therefore, we should reject the null hypothesis if the test statistic t is less than -1.6604.

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: 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 need to conduct a one-sample t-test to test if the sample mean is significantly different from the population mean (60). The null hypothesis is H₀: μ = 60, and the alternative hypothesis is H₁: μ ≠ 60. 
The test statistic can be calculated as: t = (X - μ) / (S / sqrt(n)) = (52 - 60) / (22 / sqrt(100)) = -3.64. 
Using a t-table with 99 degrees of freedom (n-1), the critical values for a two-tailed test at α = 0.05 are ±1.984. 
Since the test statistic (-3.64) falls outside the critical region, we reject the null hypothesis. 
Therefore, we can conclude that the average number of tissues used during a cold is significantly lower than 60, and the Kimberly Clark Corporation should consider packaging more than 60 tissues in each Kleenex package.

Question 7

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 8

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

We need to find the sample which gives the strongest evidence to reject the null hypothesis in favor of the alternative hypothesis. In other words, we need to find the smallest sample mean that is significantly different from the null hypothesis mean of 30.

To determine which sample gives the strongest evidence, we need to calculate the test statistic using the formula:

t = (Xbar - μ) / (S / sqrt(n))

Where Xbar is the sample mean, μ is the null hypothesis mean, S is the sample standard deviation, and n is the sample size.

The smaller the t-value, the stronger the evidence against the null hypothesis.

For sample A, t = (28 - 30) / (6 / sqrt(36)) = -1
For sample B, t = (27 - 30) / (4 / sqrt(36)) = -3
For sample C, t = (32 - 30) / (2 / sqrt(36)) = 3
For sample D, t = (26 - 30) / (9 / sqrt(36)) = -2

Therefore, sample B gives the strongest evidence to reject the null hypothesis in favor of the alternative hypothesis.

Question 9

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 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 = 0.10?
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 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 significance level is not another name for Type II error. Type II error refers to the probability of failing to reject a false null hypothesis.

Question 12

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 hypotheses to test are:
H₀: μ ≤ 30 (Mean age of customers is less than or equal to 30)
H₁: μ > 30 (Mean age of customers is greater than 30)
This is a one-tailed test because the owner is only interested in knowing if the mean age is greater than 30, not if it is simply different.

Question 13

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

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

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: 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...

Question 15

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 16

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 17

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

The null hypothesis is that the mean age of the club's customers is 30 or less. 
H₀: μ ≤ 30 
The alternative hypothesis is that the mean age of the club's customers is greater than 30. 
H₁: μ > 30 
To test this hypothesis at a level of significance of 0.01, we'll conduct a one-sample t-test. 
The test statistic is:

t = (x̄ - μ) / (s / √n) 
where x̄ = 30.45 (sample mean), μ = 30 (null hypothesis), s = 5 (sample standard deviation), and n = 250 (sample size).

t = (30.45 - 30) / (5 / √250) ≈ 2.80

The p-value for this test is P(t > 2.80) = 0.0026 (using a t-distribution with 249 degrees of freedom). 
Since the p-value is less than the level of significance (0.01), we reject the alternative hypothesis (H₁: μ > 30) and do not reject the null hypothesis (H₀: μ ≤ 30). 
Therefore, the owner should not alter the entertainment to appeal to an older crowd.

Question 18

The power of a statistical test is
A)the probability of not rejecting H₀ when it is ESQ.
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 ESQ.

Accepted Answer

The power of a statistical test is the probability of correctly rejecting the null hypothesis (H₀) when it is false, which is described in option D.

Question 19

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

The test statistic is the numerical quantity calculated from the sample data and is used to determine if the null hypothesis should be rejected or not. The significance level and critical value are related to the test statistic but are not the same thing. A parameter is a measure of a population and not a sample.

Question 20

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...

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

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 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 ESQ,then you have committed

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 we test H₀: μ = 16 versus H₁: μ ≠ 16 at α = 0.01?

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?

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?

The symbol for the power of a statistical test is

The power of a statistical test is

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.

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