Question 1

In the hypothesis H₀: μ = μ₀,the value of μ₀ is not derived from: A) the sample. B) past experience. C) a target or benchmark. D) a scientific theory.

Accepted Answer

The value of μ₀ in the hypothesis is not derived from the sample itself. It is typically predetermined based on past experience, a target or benchmark, or a scientific theory.

Question 2

The researcher's null hypotheses is H₀: σ² ≤ 22.A sample of n = 25 items yields a sample variance of s² = 28.5.The test statistic is: A) 31.09. B) 26.42. C) must know if it is a one-tailed test. D) must know α to answer.

Accepted Answer

The test statistic for testing a variance with known population mean is given by:

χ² = (n-1)s² / σ²

Substituting the given values, we get:

χ² = (25-1)(28.5) / 22 = 31.09

Therefore, the correct choice is A.

Question 3

In hypothesis testing,Type I error is: A) always set at 5 percent. B) smaller than or equal to 5 percent. C) the probability of rejecting H₀ when H₀ is true. D) the probability of rejecting H₀ when H₁ is true.

Accepted Answer

Type I error is the probability of rejecting the null hypothesis (H₀) when it is actually true. Therefore, option C is the correct choice as it gives the definition of Type I error. Option A and B are incorrect as the significance level (the probability of making a Type I error) can be set at any value, not just 5 percent. Option D is incorrect as it refers to a situation where H₁ is true, which is not relevant to the calculation of Type I error.

Question 4

In hypothesis testing,the value of β is: A) equal to 1 minus the probability of committing Type I error. B) the probability of concluding H₀ when H₀ is true. C) the probability of concluding H₀ when H₁ is true.

Accepted Answer

The value of β is the probability of committing a Type II error, which occurs when the null hypothesis (H0) is not rejected when the alternative hypothesis (H1) is true.

Question 5

Mary examined a random sample of Friday withdrawals from a college campus ATM.She hypothesized that the mean was less than $100.The results shown below are from MegaStat.What would Mary conclude from this test? Explain carefully.

Accepted Answer

The answer of Mary examined a random sample of Friday...

Question 6

Regarding the probability of Type I error (α)and Type II error (β),which statement is true?
A) β > α
B) β < α
C) α + β = 1
D) Power = 1 - β.

Accepted Answer

Power of a test is defined as 1 - β, where β is the probability of making a Type II error.

Question 7

The researcher's null hypothesis is H₀: σ² = 420.A sample of n = 18 items yields a sample variance of s² = 512.The critical values of chi-square for a two-tailed test at α = .05 are: A) 8.672 and 27.59 B) 7.564 and 30.19 C) -1.960 and +1.960 D) 9.390 and 28.87

Accepted Answer

To test the null hypothesis, we need to calculate the test statistic using the formula:
χ² = (n-1) * s² / σ²
Where n is the sample size, s² is the sample variance, and σ² is the hypothesized population variance.
Plugging in the given values, we get:
χ² = 17 * 512 / 420 = 20.57
To find the critical values for a two-tailed test at α = .05 with 17 degrees of freedom (n-1), we can use a chi-square distribution table or calculator. The critical values are approximately 7.564 and 30.19, which are the closest to option B. Therefore, we reject the null hypothesis if the test statistic falls outside this range.

Question 8

Bob hypothesizes that the average student at his university has to take more than 130 credits to graduate.He takes a random sample of his classmates and performs a test.The results shown below are from MegaStat.What would Bob conclude from this test? Explain carefully.

Accepted Answer

The answer of Bob hypothesizes that the average student at...

Question 9

Why is it better to say "fail to reject H₀" instead of "accept H₀"?

Accepted Answer

The answer of Why is it better to say "fail...

Question 10

In testing the hypotheses H₀: π ≤ π₀,H₁: π > π₀,we would use a: A) two-tailed test. B) left-tailed test. C) right-tailed test. D) breathalyzer test.

Accepted Answer

The hypotheses suggest that the population parameter π is greater than a certain value. This means we are interested in the right tail of the sampling distribution. Therefore, a right-tailed test is appropriate.

Question 11

Julia hypothesizes that fewer than 90 percent of her Visa purchases are under $100.She examines a random sample of her recent purchases and performs a test.The results shown below are from MegaStat.What would Julia conclude from this test? Explain carefully.

Accepted Answer

The answer of Julia hypothesizes that fewer than 90 percent...

Question 12

For a right-tailed test of hypothesis for a population mean with known σ,the test statistic was z = 1.79.The p-value is:
A) .0367
B) .9633
C) .1186
D) .0179

Accepted Answer

For a right-tailed test, the p-value is the area to the right of the test statistic. Using a standard normal distribution table, the area to the right of 1.79 is approximately 0.0367.

Question 13

The researcher's null hypotheses is H₀: σ² = 420.A sample of n = 18 items yields a sample variance of s² = 512.The test statistic is: A) 34.09 B) 20.72 C) 14.77 D) must know α to answer.

Accepted Answer

The answer of The researcher's null hypotheses is H₀: σ²...

Question 14

We can assume that the sample proportion is normally distributed if:
A) we have 10 successes in the sample.
B) we have 10 failures in the sample.
C) we have both 10 successes and 10 failures in the sample.
D) the population is known.

Accepted Answer

According to the central limit theorem, if we have a sample size of at least 30 or if we have both successes and failures that are greater than or equal to 10, the sample proportion can be assumed to be normally distributed. Therefore, choice C is the best choice as it satisfies this condition.

Question 15

Pedro hypothesizes that more than half of his classmates would prefer a virtual web graduation ceremony,rather than sitting in the hot sun during the commencement speech.He takes a random sample of his classmates and performs a test.The results shown below are from MegaStat.What would Pedro conclude from this test? Explain carefully.

Accepted Answer

The answer of Pedro hypothesizes that more than half of...

Question 16

The researcher's null hypothesis is H₀: σ² ≤ 22.A sample of n = 25 items yields a sample variance of s² = 28.5.The critical value of chi-square for a right-tailed test at α = 05 is: A) 1.960 B) 1.645 C) 13.85 D) 36.42

Accepted Answer

To find the critical value of chi-square, we need to use the formula:

χ^2 = (n-1) * s^2 / σ^2

where n is the sample size, s^2 is the sample variance, and σ^2 is the hypothesized population variance.

Substituting the given values, we get:

χ^2 = (25-1) * 28.5 / 22 ≤ 31.4068

To find the critical value of chi-square for a right-tailed test at α = .05, we need to look up the value in the chi-square distribution table with (25-1) degrees of freedom and a probability of 0.95 (1-α). The closest value is 36.42, which corresponds to a probability of 0.95.

Therefore, the best choice is D, 36.42, because it is the critical value of chi-square for a right-tailed test at α = .05 with (25-1) degrees of freedom.

Quiz 9: One-Sample Hypothesis Tests

In the hypothesis H₀: μ = μ₀,the value of μ₀ is not derived from:

The researcher's null hypotheses is H₀: σ² ≤ 22.A sample of n = 25 items yields a sample variance of s² = 28.5.The test statistic is:

In hypothesis testing,Type I error is:

In hypothesis testing,the value of β is:

Mary examined a random sample of Friday withdrawals from a college campus ATM.She hypothesized that the mean was less than $100.The results shown below are from MegaStat.What would Mary conclude from this test? Explain carefully.

Regarding the probability of Type I error (α) and Type II error (β) ,which statement is true?

The researcher's null hypothesis is H₀: σ² = 420.A sample of n = 18 items yields a sample variance of s² = 512.The critical values of chi-square for a two-tailed test at α = .05 are:

Bob hypothesizes that the average student at his university has to take more than 130 credits to graduate.He takes a random sample of his classmates and performs a test.The results shown below are from MegaStat.What would Bob conclude from this test? Explain carefully.

Why is it better to say "fail to reject H₀" instead of "accept H₀"?

In testing the hypotheses H₀: π ≤ π₀,H₁: π > π₀,we would use a:

Julia hypothesizes that fewer than 90 percent of her Visa purchases are under $100.She examines a random sample of her recent purchases and performs a test.The results shown below are from MegaStat.What would Julia conclude from this test? Explain carefully.

For a right-tailed test of hypothesis for a population mean with known σ,the test statistic was z = 1.79.The p-value is:

The researcher's null hypotheses is H₀: σ² = 420.A sample of n = 18 items yields a sample variance of s² = 512.The test statistic is:

We can assume that the sample proportion is normally distributed if:

The researcher's null hypothesis is H₀: σ² ≤ 22.A sample of n = 25 items yields a sample variance of s² = 28.5.The critical value of chi-square for a right-tailed test at α = 05 is:

Quiz 9: One-Sample Hypothesis Tests

In the hypothesis H0: μ = μ0,the value of μ0 is not derived from:

The researcher's null hypotheses is H0: σ2 ≤ 22.A sample of n = 25 items yields a sample variance of s2 = 28.5.The test statistic is:

In hypothesis testing,Type I error is:

In hypothesis testing,the value of β is:

Mary examined a random sample of Friday withdrawals from a college campus ATM.She hypothesized that the mean was less than $100.The results shown below are from MegaStat.What would Mary conclude from this test? Explain carefully.

Regarding the probability of Type I error (α) and Type II error (β) ,which statement is true?

The researcher's null hypothesis is H0: σ2 = 420.A sample of n = 18 items yields a sample variance of s2 = 512.The critical values of chi-square for a two-tailed test at α = .05 are:

Bob hypothesizes that the average student at his university has to take more than 130 credits to graduate.He takes a random sample of his classmates and performs a test.The results shown below are from MegaStat.What would Bob conclude from this test? Explain carefully.

Why is it better to say "fail to reject H0" instead of "accept H0"?

In testing the hypotheses H0: π ≤ π0,H1: π > π0,we would use a:

Julia hypothesizes that fewer than 90 percent of her Visa purchases are under $100.She examines a random sample of her recent purchases and performs a test.The results shown below are from MegaStat.What would Julia conclude from this test? Explain carefully.

For a right-tailed test of hypothesis for a population mean with known σ,the test statistic was z = 1.79.The p-value is:

The researcher's null hypotheses is H0: σ2 = 420.A sample of n = 18 items yields a sample variance of s2 = 512.The test statistic is:

We can assume that the sample proportion is normally distributed if:

The researcher's null hypothesis is H0: σ2 ≤ 22.A sample of n = 25 items yields a sample variance of s2 = 28.5.The critical value of chi-square for a right-tailed test at α = 05 is:

In the hypothesis H₀: μ = μ₀,the value of μ₀ is not derived from:

The researcher's null hypotheses is H₀: σ² ≤ 22.A sample of n = 25 items yields a sample variance of s² = 28.5.The test statistic is:

The researcher's null hypothesis is H₀: σ² = 420.A sample of n = 18 items yields a sample variance of s² = 512.The critical values of chi-square for a two-tailed test at α = .05 are:

Why is it better to say "fail to reject H₀" instead of "accept H₀"?

In testing the hypotheses H₀: π ≤ π₀,H₁: π > π₀,we would use a:

The researcher's null hypotheses is H₀: σ² = 420.A sample of n = 18 items yields a sample variance of s² = 512.The test statistic is:

The researcher's null hypothesis is H₀: σ² ≤ 22.A sample of n = 25 items yields a sample variance of s² = 28.5.The critical value of chi-square for a right-tailed test at α = 05 is: