Question 1

A researcher tests the mean of a sample of 28 people and calculates a value of 2.13 for the t-statistic. For α = .05 (two-tailed), which of the following decisions is MOST appropriate?
A) do not reject null (p < .05)
B) do not reject null (p > .05)
C) reject null (p < .05)
D) accept null (p < .05)

Accepted Answer

In order to make a decision about whether to reject or fail to reject the null hypothesis, we need to compare the calculated value of the t-statistic to a critical value of t from a t-distribution table using the degrees of freedom (df) which is the sample size n minus 1 (df=28-1=27).

At α=.05 with two tails, the critical value for a t-distribution with 27 df is ±2.048. Since the calculated value of the t-statistic (2.13) is greater than the critical value of t (2.048), we reject the null hypothesis. This means that there is sufficient evidence to conclude that the population mean is not equal to the hypothesized value. Therefore, the most appropriate decision is to reject the null hypothesis, which is choice C.

Question 2

If the value of a t-statistic falls between the critical values for α = .05 and α = .01, you would describe the level of significance as ______. A) p > .01 B) p > .05 C) p < .01 D) p < .05

Accepted Answer

The level of significance is the probability of rejecting the null hypothesis when it is true. The critical values for α = .05 and α = .01 are the values of the t-statistic that correspond to a probability of .05 and .01, respectively. If the value of the t-statistic falls between these two values, then the probability of rejecting the null hypothesis when it is true is between .05 and .01. This means that the level of significance is less than .01.

Question 3

A researcher tests the mean of a sample of 22 people and calculates a value of 1.81 for the t-statistic. For α = .05 (two-tailed), which of the following decisions is MOST appropriate? A) do not reject null (p < .05) B) do not reject null (p > .05) C) reject null (p < .05) D) reject null (p > .05)

Accepted Answer

With a t-statistic of 1.81 and a sample size of 22, the degrees of freedom would be 21. For a two-tailed test at α = .05, the critical t-value would typically be higher than 1.81 (exact value depends on the t-distribution table). Since the calculated t-statistic does not exceed the critical value, the p-value would be greater than .05, leading to the decision not to reject the null hypothesis.

Question 4

A researcher calculates a mean from a sample of 18 people. In analyzing her data, she states the following hypotheses: H₀: μ = 20 and H₁: μ ≠ 20. For α = .05, which is an appropriate critical value? A) 1.734 B) 2.110 C) 2.101 D) 2.086

Accepted Answer

Given that the sample size is 18, the degrees of freedom for the t-test would be 17 (n-1). For a two-tailed test with α = .05, the critical value from the t-distribution table for 17 degrees of freedom is approximately 2.110.

Question 5

A researcher calculates a mean from a sample of 23 people. In analyzing her data, she states the following hypotheses: H₀: μ = 25 and H₁: μ ≠ 25. For α = .05, which is an appropriate critical value? A) 1.717 B) 2.074 C) 2.069 D) 2.064

Accepted Answer

Since the researcher is using a two-tailed test with a significance level of α = .05, the appropriate critical value for a t-test with 22 degrees of freedom (sample size - 1) is 2.074. This critical value can be found in a t-table or using a statistical software program. Therefore, the best choice is B.

Question 6

A researcher calculates a mean from a sample of 15 people. In analyzing her data, she states the following hypotheses: H₀: μ = 25 and H₁: μ ≠ 25. If α = .05, which of the following is an appropriate critical value? A) 1.709 B) 1.753 C) 2.060 D) 2.145

Accepted Answer

The answer of A researcher calculates a mean from a...

Question 7

A researcher tests the mean of a sample of 16 people and calculates a value of 2.42 for the t-statistic. For α = .05 (two-tailed), which of the following is the MOST appropriate level of significance? A) p < .05 B) p > .05 C) p < .01 D) p > .01

Accepted Answer

Given a t-statistic of 2.42 with a sample size of 16 (implying 15 degrees of freedom for a two-tailed test at α = .05), the p-value would be less than .05, indicating that the result is statistically significant at the .05 level but not necessarily at the .01 level.

Question 8

A researcher calculates a mean from a sample of 19 people. For α = .05, if the researcher states the hypotheses as H₀: µ = 200 and H₁: µ < 200, which of the following is an appropriate critical value? A) 0.688 B) 1.645 C) 1.734 D) 1.729

Accepted Answer

Given that the sample size is 19 (which means degrees of freedom = 18) and the test is one-tailed with α = .05, the appropriate critical value from the t-distribution table for a one-tailed test with these parameters is approximately 1.734.

Question 9

A researcher calculates a mean from a sample of 21 people. In analyzing her data, she states the following hypotheses: H₀: μ = 16 and H₁: μ ≠ 16. For α = .05, which is an appropriate critical value? A) 1.725 B) 2.086 C) 2.093 D) 2.131

Accepted Answer

The answer of A researcher calculates a mean from a...

Question 10

You test the mean of a sample of 19 people and calculate a value of 2.14 for the t-statistic. For α = .05 (two-tailed), which of the following decisions is MOST appropriate?
A) do not reject null (p > .01)
B) reject null (p > .05)
C) accept alternative (p > .05)
D) reject null (p < .05)

Accepted Answer

For a two-tailed test with 18 degrees of freedom (n-1 = 19-1), the critical t-value at α = .05 is approximately ±2.101. Since the calculated t-statistic of 2.14 is greater than 2.101, we reject the null hypothesis at the 0.05 significance level.

Question 11

A researcher calculates a value of 3.21 for a t-statistic. For df = 20 and alpha = .05 (two-tailed), which of the following is the MOST accurate?
A) reject the null hypothesis
B) p < .05
C) p < .01
D) do not reject the null hypothesis

Accepted Answer

The answer of A researcher calculates a value of 3.21...

Question 12

A researcher calculates a mean from a sample of 24 people. In analyzing her data, she states the following hypotheses: H₀: μ = 20 and H₁: μ ≠ 20. For α = .05, what is the appropriate critical value for her statistic? A) 1.714 B) 2.086 C) 2.069 D) 2.064

Accepted Answer

The appropriate critical value for a two-tailed test with α = .05 and degrees of freedom (df) = 23 (since df = n - 1 for a sample size of 24) is 2.069, which corresponds to the t-distribution critical value for these parameters.

Question 13

Imagine the value of a t-statistic is greater than the critical value for α = .05 but less than the critical value for α = .01. Which of the following is the level of significance for this t-statistic? A) p < .01 (but not < .05) B) p > .01 C) p > .01 (but not < .05) D) p < .05 (but not < .01)

Accepted Answer

The t-statistic is significant at the .05 level (since it is greater than the critical value for α = .05), but not significant at the .01 level (since it is less than the critical value for α = .01). Therefore, the p-value must be between .01 and .05, so the correct choice is D.

Question 14

Another researcher calculates a mean from a sample of 25 people. For α = .05, if he states the hypotheses as H₀: μ = 100 and H₁: μ < 100, which of the following is an appropriate critical value? A) 1.714 B) 1.711 C) 1.708 D) 2.060

Accepted Answer

The answer of Another researcher calculates a mean from a...

Question 15

You calculate a value of 1.17 for the t-statistic and find falls in the region of non-rejection. As a result, the most appropriate conclusion is that you ______.
A) do not reject the alternative hypothesis
B) reject the null hypothesis
C) reject the alternative hypothesis
D) do not reject the null hypothesis

Accepted Answer

A t-statistic falling in the region of non-rejection means that the calculated t-value does not exceed the critical t-value in the rejection region. Therefore, we fail to reject the null hypothesis and accept it as true. The correct answer is D - do not reject the null hypothesis.

Question 16

A researcher calculates a mean from a sample of 10 people. In analyzing her data, she states the following hypotheses: H₀: μ = 30 and H₁: μ ≠ 30. If α = .05, which of the following is an appropriate critical value? A) 1.833 B) 2.042 C) 2.228 D) 2.262

Accepted Answer

The answer of A researcher calculates a mean from a...

Question 17

If the value of the t-statistic calculated from a set of data ______ the critical value, you would say ______.
A) exceeds; p < .05
B) exceeds; p > .05
C) does not exceed; p < .05
D) does not exceed; p < .01

Accepted Answer

If the value of the t-statistic calculated from a set of data exceeds the critical value, then we reject the null hypothesis and accept the alternative hypothesis at the 0.05 significance level, which is represented by p < .05.

Question 18

Imagine the value of a t-statistic is less than the critical value for α = .01 but greater than the critical value for α = .05. Which of the following is the MOST appropriate way to report the level of significance? A) p < .01 B) p > .01 C) p > .05 D) p < .05

Accepted Answer

Since the t-statistic is greater than the critical value for α = .05, we can reject the null hypothesis at the .05 level of significance. Therefore, p < .05 is the appropriate way to report the level of significance. However, we cannot reject the null hypothesis at the .01 level of significance, so p > .01 and p > .05 are not valid choices.

Question 19

A researcher tests the mean of a sample of 24 people and calculates a value of 1.98 for the t-statistic. For α = .05 (two-tailed), which of the following decisions is MOST appropriate?
A) do not reject null (p > .01)
B) do not reject null (p > .05)
C) reject null (p < .05)
D) reject null (p > .05)

Accepted Answer

Given the t-statistic value of 1.98 and a sample size of 24 (which implies 23 degrees of freedom for a t-test), the p-value would be greater than .05 but less than .10 for a two-tailed test. Therefore, at an alpha level of .05, we do not have sufficient evidence to reject the null hypothesis, making option B the most appropriate decision.

Question 20

A researcher tests the mean of a sample of 25 people and calculates a value of 2.51 for the t-statistic. For α = .05 (two-tailed), which of the following is most appropriate? A) do not reject null (p < .05) B) do not reject null (p > .05) C) reject null (p < .05) D) reject null (p > .01)

Accepted Answer

For α = .05 (two-tailed) and a sample size of 25, the critical t-value is approximately ±2.064 per t-distribution table. Since the calculated t-value of 2.51 is greater than the critical t-value of 2.064, we reject the null hypothesis. The p-value associated with this t-value is less than .05 (since a one-tailed test would have a p-value less than .025), which also supports rejecting the null hypothesis. Therefore, the most appropriate choice is to reject the null hypothesis, which is choice C.

Quiz 7: Testing One Sample Mean

A researcher tests the mean of a sample of 28 people and calculates a value of 2.13 for the t-statistic. For α = .05 (two-tailed) , which of the following decisions is MOST appropriate?

If the value of a t-statistic falls between the critical values for α = .05 and α = .01, you would describe the level of significance as ______.

A researcher tests the mean of a sample of 22 people and calculates a value of 1.81 for the t-statistic. For α = .05 (two-tailed) , which of the following decisions is MOST appropriate?

A researcher calculates a mean from a sample of 18 people. In analyzing her data, she states the following hypotheses: H₀: μ = 20 and H₁: μ ≠ 20. For α = .05, which is an appropriate critical value?

A researcher calculates a mean from a sample of 23 people. In analyzing her data, she states the following hypotheses: H₀: μ = 25 and H₁: μ ≠ 25. For α = .05, which is an appropriate critical value?

A researcher calculates a mean from a sample of 15 people. In analyzing her data, she states the following hypotheses: H₀: μ = 25 and H₁: μ ≠ 25. If α = .05, which of the following is an appropriate critical value?

A researcher tests the mean of a sample of 16 people and calculates a value of 2.42 for the t-statistic. For α = .05 (two-tailed) , which of the following is the MOST appropriate level of significance?

A researcher calculates a mean from a sample of 19 people. For α = .05, if the researcher states the hypotheses as H₀: µ = 200 and H₁: µ < 200, which of the following is an appropriate critical value?

A researcher calculates a mean from a sample of 21 people. In analyzing her data, she states the following hypotheses: H₀: μ = 16 and H₁: μ ≠ 16. For α = .05, which is an appropriate critical value?

You test the mean of a sample of 19 people and calculate a value of 2.14 for the t-statistic. For α = .05 (two-tailed) , which of the following decisions is MOST appropriate?

A researcher calculates a value of 3.21 for a t-statistic. For df = 20 and alpha = .05 (two-tailed) , which of the following is the MOST accurate?

A researcher calculates a mean from a sample of 24 people. In analyzing her data, she states the following hypotheses: H₀: μ = 20 and H₁: μ ≠ 20. For α = .05, what is the appropriate critical value for her statistic?

Imagine the value of a t-statistic is greater than the critical value for α = .05 but less than the critical value for α = .01. Which of the following is the level of significance for this t-statistic?

Another researcher calculates a mean from a sample of 25 people. For α = .05, if he states the hypotheses as H₀: μ = 100 and H₁: μ < 100, which of the following is an appropriate critical value?

You calculate a value of 1.17 for the t-statistic and find falls in the region of non-rejection. As a result, the most appropriate conclusion is that you ______.

A researcher calculates a mean from a sample of 10 people. In analyzing her data, she states the following hypotheses: H₀: μ = 30 and H₁: μ ≠ 30. If α = .05, which of the following is an appropriate critical value?

If the value of the t-statistic calculated from a set of data the critical value, you would say .

Imagine the value of a t-statistic is less than the critical value for α = .01 but greater than the critical value for α = .05. Which of the following is the MOST appropriate way to report the level of significance?

A researcher tests the mean of a sample of 24 people and calculates a value of 1.98 for the t-statistic. For α = .05 (two-tailed) , which of the following decisions is MOST appropriate?

A researcher tests the mean of a sample of 25 people and calculates a value of 2.51 for the t-statistic. For α = .05 (two-tailed) , which of the following is most appropriate?

Quiz 7: Testing One Sample Mean

A researcher tests the mean of a sample of 28 people and calculates a value of 2.13 for the t-statistic. For α = .05 (two-tailed) , which of the following decisions is MOST appropriate?

If the value of a t-statistic falls between the critical values for α = .05 and α = .01, you would describe the level of significance as ______.

A researcher tests the mean of a sample of 22 people and calculates a value of 1.81 for the t-statistic. For α = .05 (two-tailed) , which of the following decisions is MOST appropriate?

A researcher calculates a mean from a sample of 18 people. In analyzing her data, she states the following hypotheses: H0: μ = 20 and H1: μ ≠ 20. For α = .05, which is an appropriate critical value?

A researcher calculates a mean from a sample of 23 people. In analyzing her data, she states the following hypotheses: H0: μ = 25 and H1: μ ≠ 25. For α = .05, which is an appropriate critical value?

A researcher calculates a mean from a sample of 15 people. In analyzing her data, she states the following hypotheses: H0: μ = 25 and H1: μ ≠ 25. If α = .05, which of the following is an appropriate critical value?

A researcher tests the mean of a sample of 16 people and calculates a value of 2.42 for the t-statistic. For α = .05 (two-tailed) , which of the following is the MOST appropriate level of significance?

A researcher calculates a mean from a sample of 19 people. For α = .05, if the researcher states the hypotheses as H0: µ = 200 and H1: µ < 200, which of the following is an appropriate critical value?

A researcher calculates a mean from a sample of 21 people. In analyzing her data, she states the following hypotheses: H0: μ = 16 and H1: μ ≠ 16. For α = .05, which is an appropriate critical value?

You test the mean of a sample of 19 people and calculate a value of 2.14 for the t-statistic. For α = .05 (two-tailed) , which of the following decisions is MOST appropriate?

A researcher calculates a value of 3.21 for a t-statistic. For df = 20 and alpha = .05 (two-tailed) , which of the following is the MOST accurate?

A researcher calculates a mean from a sample of 24 people. In analyzing her data, she states the following hypotheses: H0: μ = 20 and H1: μ ≠ 20. For α = .05, what is the appropriate critical value for her statistic?

Imagine the value of a t-statistic is greater than the critical value for α = .05 but less than the critical value for α = .01. Which of the following is the level of significance for this t-statistic?

Another researcher calculates a mean from a sample of 25 people. For α = .05, if he states the hypotheses as H0: μ = 100 and H1: μ < 100, which of the following is an appropriate critical value?

You calculate a value of 1.17 for the t-statistic and find falls in the region of non-rejection. As a result, the most appropriate conclusion is that you ______.

A researcher calculates a mean from a sample of 10 people. In analyzing her data, she states the following hypotheses: H0: μ = 30 and H1: μ ≠ 30. If α = .05, which of the following is an appropriate critical value?

If the value of the t-statistic calculated from a set of data ______ the critical value, you would say ______.

Imagine the value of a t-statistic is less than the critical value for α = .01 but greater than the critical value for α = .05. Which of the following is the MOST appropriate way to report the level of significance?

A researcher tests the mean of a sample of 24 people and calculates a value of 1.98 for the t-statistic. For α = .05 (two-tailed) , which of the following decisions is MOST appropriate?

A researcher tests the mean of a sample of 25 people and calculates a value of 2.51 for the t-statistic. For α = .05 (two-tailed) , which of the following is most appropriate?

A researcher calculates a mean from a sample of 18 people. In analyzing her data, she states the following hypotheses: H₀: μ = 20 and H₁: μ ≠ 20. For α = .05, which is an appropriate critical value?

A researcher calculates a mean from a sample of 23 people. In analyzing her data, she states the following hypotheses: H₀: μ = 25 and H₁: μ ≠ 25. For α = .05, which is an appropriate critical value?

A researcher calculates a mean from a sample of 15 people. In analyzing her data, she states the following hypotheses: H₀: μ = 25 and H₁: μ ≠ 25. If α = .05, which of the following is an appropriate critical value?

A researcher calculates a mean from a sample of 19 people. For α = .05, if the researcher states the hypotheses as H₀: µ = 200 and H₁: µ < 200, which of the following is an appropriate critical value?

A researcher calculates a mean from a sample of 21 people. In analyzing her data, she states the following hypotheses: H₀: μ = 16 and H₁: μ ≠ 16. For α = .05, which is an appropriate critical value?

A researcher calculates a mean from a sample of 24 people. In analyzing her data, she states the following hypotheses: H₀: μ = 20 and H₁: μ ≠ 20. For α = .05, what is the appropriate critical value for her statistic?

Another researcher calculates a mean from a sample of 25 people. For α = .05, if he states the hypotheses as H₀: μ = 100 and H₁: μ < 100, which of the following is an appropriate critical value?

A researcher calculates a mean from a sample of 10 people. In analyzing her data, she states the following hypotheses: H₀: μ = 30 and H₁: μ ≠ 30. If α = .05, which of the following is an appropriate critical value?

If the value of the t-statistic calculated from a set of data the critical value, you would say .