Question 1

In hypothesis testing if the null hypothesis is rejected,
A) no conclusions can be drawn from the test
B) the alternative hypothesis is true
C) the data must have been accumulated incorrectly
D) the sample size has been too small

Accepted Answer

If the null hypothesis is rejected, it means that there is enough evidence to support the alternative hypothesis. However, it does not mean that the alternative hypothesis is true with absolute certainty, only that it is more likely to be true than the null hypothesis based on the available evidence.

Question 2

We are interested in testing the following hypotheses. H0: μ1- μ2 ≥ 0 Ha: μ1- μ2 < 0
Based on 40 degrees of freedom, the test statistic t is computed to be 2.423. The p-value for this test is
A) 0.01
B) 0.02
C) 0.025
D) between 0.025 to 0.05

Accepted Answer

The p-value for a two-tailed test with a test statistic of 2.423 and 40 degrees of freedom is approximately 0.02.

Question 3

For a one-tailed test lower tail) at 93.7% confidence, Z =
A) -1.86
B) -1.53
C) -1.96
D) -1.645

Accepted Answer

For a one-tailed test at 93.7% confidence level, the corresponding Z-value is the 6.3rd percentile which can be found using a standard normal table or calculator. This Z-value is -1.53 which falls closest to choice B.

Question 4

We are interested in testing the following hypotheses. H0: μ1- μ2 = 0 Ha: μ1- μ2 ? 0
The test statistic Z is computed to be 1.85. The p-value for this test is
A) 0.4678
B) 0.9678
C) 0.0322
D) 0.0644

Accepted Answer

The test is two-tailed, and the Z value of 1.85 corresponds to a p-value of 0.0322 for one tail. Therefore, for two tails, the p-value is 0.0644.

Question 5

If the p-value is larger than 1,
A) the null hypothesis must be rejected.
B) the alternative hypothesis must be accepted.
C) the value of Z must be zero.
D) a mistake must have been made in computations.

Accepted Answer

A p-value cannot be larger than 1 as it represents the probability of observing the test statistic or a more extreme value under the null hypothesis. If the p-value is larger than 1, it indicates an error in the computations.

Question 6

When the following hypotheses are being tested at a level of significance of α, H0: μ1- μ2 ≥ 0 Ha: μ1- μ2 < 0
The null hypothesis will be rejected if the p-value is
A) 1 − α
B) > α
C) > α/2
D) ≤ α

Accepted Answer

The null hypothesis will be rejected if the p-value is less than or equal to α, since this means that the observed difference between the means is unlikely to have occurred by chance alone.

Question 7

For a two-tailed test at 98.5% confidence, Z =
A) ± 2.17
B) ± 1.96
C) ± 2.98
D) ± 2.43

Accepted Answer

For a two-tailed test at 98.5% confidence, the critical Z-value is approximately ±2.43. This is because the confidence level of 98.5% leaves 1.5% in the tails, or 0.75% in each tail, which corresponds to a Z-value of ±2.43.

Question 8

The p-value
A) is the same as the Z statistic
B) measures the number of standard deviations from the mean
C) is a distance
D) is a probability

Accepted Answer

The p-value is the probability of observing a test statistic at least as extreme as the one calculated from the sample data, assuming the null hypothesis is true. It is a measure of the strength of evidence against the null hypothesis. Higher p-values indicate weaker evidence against the null hypothesis, while lower p-values indicate stronger evidence against the null hypothesis. Therefore, the p-value is a probability, not a Z statistic, distance, or number of standard deviations from the mean.

Question 9

We are interested in testing the following hypotheses. H0: μ1- μ2 ≥ 0 Ha: μ1- μ2 < 0
The test statistic Z is computed to be 2.83. The p-value for this test is
A) 0.4977
B) 0.0023
C) 0.0046
D) 0.9977

Accepted Answer

With Ha: μ1- μ2 < 0, this is a one-tailed test with the alternative hypothesis stating that the difference between the means is less than zero. A Z-score of 2.83 corresponds to a p-value of approximately 0.0023. Since this p-value is less than the commonly used level of significance of 0.05, we reject the null hypothesis H0: μ1- μ2 ≥ 0 and conclude that there is sufficient evidence to suggest that the population mean of group 1 is significantly less than the population mean of group 2. Therefore, the best choice is B.

Question 10

If a hypothesis is rejected at 95% confidence, it
A) will not be rejected at 90% confidence
B) will also be rejected at 90% confidence
C) will sometimes be rejected at 90% confidence
D) None of these alternatives is correct.

Accepted Answer

If a hypothesis is rejected at 95% confidence level, it means that there is only a 5% chance that the observed results occurred by chance. This rejection is a stronger conclusion than not rejecting the hypothesis. Therefore, if we lower the confidence level to 90%, the likelihood of accepting the hypothesis increases, but if the hypothesis was rejected at 95%, it will still be rejected at 90%. So, the correct answer is B, the hypothesis will also be rejected at 90% confidence level.

Question 11

For a two-tailed test at 86.12% confidence, Z =
A) 1.96
B) 1.48
C) 1.09
D) 0.8612

Accepted Answer

The answer of For a two-tailed test at 86.12% confidence,...

Question 12

Which of the following does not need to be known in order to compute the p-value?
A) knowledge of whether the test is one-tailed or two-tailed
B) the value of the test statistic
C) the level of significance
D) None of these alternatives is correct.

Accepted Answer

The answer of Which of the following does not need...

Question 13

When the p-value is used for hypothesis testing, the null hypothesis is not rejected if the
A) p­value ≤ α
B) p­value > α
C) p­value ≥ 1
D) p-value < 0

Accepted Answer

The p-value is compared with the significance level (α) to make a decision about the null hypothesis. If the p-value is greater than α, we fail to reject the null hypothesis, as we do not have enough evidence to prove that the alternative hypothesis is true. Only when the p-value is less than or equal to α, we reject the null hypothesis in favor of the alternative hypothesis. Thus, option B is the correct choice.

Question 14

In order to test the following hypotheses at an α level of significance, H0: μ1- μ2 ≤ 0 Ha: μ1- μ2 > 0
The null hypothesis will be rejected if the test statistic Z is
A) ≤ Zα
B) ≥ Zα
C) < -Zα
D) < 0

Accepted Answer

Since the alternative hypothesis is one-tailed and greater than sign (>), we need to look for the critical value of Z from the right-hand side of the standard normal distribution table. This critical value is Zα, which represents the value such that the area to the right of Zα under the standard normal curve is α.

Therefore, if the test statistic Z is greater than or equal to the critical value Zα, we would reject the null hypothesis in favor of the alternative hypothesis at the α level of significance.

Hence, the correct answer is B, which states that the null hypothesis will be rejected if the test statistic Z is greater than or equal to Zα.

Question 15

For a one-tailed test lower tail) at 99.7% confidence, Z =
A) ± 1.86
B) - 2.75
C) ±1.96
D) -1.645

Accepted Answer

For a one-tailed lower tail test at 99.7% confidence, we look for the Z-score that leaves 0.3% in the lower tail. This corresponds to a Z-score of approximately -2.75.

Question 16

When the p-value is used for hypothesis testing, the null hypothesis is rejected if
A) p-value ≤ α
B) α < p-value
C) p-value ≥ α
D) p-value = 1 - α

Accepted Answer

The p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the observed value, assuming the null hypothesis is true. If the p-value is less than or equal to the chosen significance level (usually denoted as α), then the null hypothesis is rejected in favor of the alternative hypothesis. Therefore, the correct choice is A - the null hypothesis is rejected if p-value ≤ α.

Question 17

The p-value
A) ranges between minus infinity to plus infinity
B) ranges between minus 1 to plus 1
C) is larger than 1
D) ranges between 0 to 1

Accepted Answer

The p-value ranges between 0 and 1, and represents the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true. A p-value less than the predetermined significance level (usually 0.05) indicates strong evidence against the null hypothesis, while a p-value greater than the significance level does not provide sufficient evidence to reject the null hypothesis. Therefore, a p-value outside the 0 to 1 range would not make sense in the context of hypothesis testing.

Question 18

We are interested in testing the following hypotheses. H0: μ1­ μ2 = 0
Ha: μ1­ μ2 ≠ 0
The test statistic Z is computed to be 2.00. The p-value for this test is
A) 0.9772
B) 1.9544
C) 0.0228
D) 0.0456

Accepted Answer

The answer of We are interested in testing the following...

Question 19

The level of significance
A) can be any positive value
B) can be any value
C) is 1 - confidence level)
D) can be any value between -1.96 to 1.96

Accepted Answer

The level of significance is the probability of rejecting a true null hypothesis. It is closely related to the confidence level, which is the probability of accepting a true null hypothesis. Thus, the level of significance is equal to 1 minus the confidence level. It cannot be any positive value, any value, or between -1.96 to 1.96.

Question 20

When using inference regarding two population means for "matched samples," the following values were found for d = Score After - Score Before: 2, -4, 1, 2, -1
The test statistics for this situation is
A) 0
B) 1
C) Since the confidence level is not known, it cannot be answered.
D) Not enough information is given to answer this question.

Accepted Answer

The test statistic for matched samples is the mean of the differences between the two scores for each subject. In this case, the mean of the differences is 0, so the test statistic is 0.

Quiz 10: Comparisons Involving Means, Experimental Design, and Analysis of Variance

In hypothesis testing if the null hypothesis is rejected,

We are interested in testing the following hypotheses. H0: μ1- μ2 ≥ 0 Ha: μ1- μ2 < 0 Based on 40 degrees of freedom, the test statistic t is computed to be 2.423. The p-value for this test is

For a one-tailed test lower tail) at 93.7% confidence, Z =

We are interested in testing the following hypotheses. H0: μ1- μ2 = 0 Ha: μ1- μ2 ? 0 The test statistic Z is computed to be 1.85. The p-value for this test is

If the p-value is larger than 1,

When the following hypotheses are being tested at a level of significance of α, H0: μ1- μ2 ≥ 0 Ha: μ1- μ2 < 0 The null hypothesis will be rejected if the p-value is

For a two-tailed test at 98.5% confidence, Z =

The p-value

We are interested in testing the following hypotheses. H0: μ1- μ2 ≥ 0 Ha: μ1- μ2 < 0 The test statistic Z is computed to be 2.83. The p-value for this test is

If a hypothesis is rejected at 95% confidence, it

For a two-tailed test at 86.12% confidence, Z =

Which of the following does not need to be known in order to compute the p-value?

When the p-value is used for hypothesis testing, the null hypothesis is not rejected if the

In order to test the following hypotheses at an α level of significance, H0: μ1- μ2 ≤ 0 Ha: μ1- μ2 > 0 The null hypothesis will be rejected if the test statistic Z is

For a one-tailed test lower tail) at 99.7% confidence, Z =

When the p-value is used for hypothesis testing, the null hypothesis is rejected if

The p-value

We are interested in testing the following hypotheses. H0: μ1 μ2 = 0 Ha: μ1 μ2 ≠ 0 The test statistic Z is computed to be 2.00. The p-value for this test is

The level of significance

When using inference regarding two population means for "matched samples," the following values were found for d = Score After - Score Before: 2, -4, 1, 2, -1 The test statistics for this situation is

Quiz 10: Comparisons Involving Means, Experimental Design, and Analysis of Variance

In hypothesis testing if the null hypothesis is rejected,

We are interested in testing the following hypotheses. H0: μ1- μ2 ≥ 0 Ha: μ1- μ2 < 0 Based on 40 degrees of freedom, the test statistic t is computed to be 2.423. The p-value for this test is

For a one-tailed test lower tail) at 93.7% confidence, Z =

We are interested in testing the following hypotheses. H0: μ1- μ2 = 0 Ha: μ1- μ2 ? 0 The test statistic Z is computed to be 1.85. The p-value for this test is

If the p-value is larger than 1,

When the following hypotheses are being tested at a level of significance of α, H0: μ1- μ2 ≥ 0 Ha: μ1- μ2 < 0 The null hypothesis will be rejected if the p-value is

For a two-tailed test at 98.5% confidence, Z =

The p-value

We are interested in testing the following hypotheses. H0: μ1- μ2 ≥ 0 Ha: μ1- μ2 < 0 The test statistic Z is computed to be 2.83. The p-value for this test is

If a hypothesis is rejected at 95% confidence, it

For a two-tailed test at 86.12% confidence, Z =

Which of the following does not need to be known in order to compute the p-value?

When the p-value is used for hypothesis testing, the null hypothesis is not rejected if the

In order to test the following hypotheses at an α level of significance, H0: μ1- μ2 ≤ 0 Ha: μ1- μ2 > 0 The null hypothesis will be rejected if the test statistic Z is

For a one-tailed test lower tail) at 99.7% confidence, Z =

When the p-value is used for hypothesis testing, the null hypothesis is rejected if

The p-value

We are interested in testing the following hypotheses. H0: μ1­ μ2 = 0 Ha: μ1­ μ2 ≠ 0 The test statistic Z is computed to be 2.00. The p-value for this test is

The level of significance

When using inference regarding two population means for "matched samples," the following values were found for d = Score After - Score Before: 2, -4, 1, 2, -1 The test statistics for this situation is

We are interested in testing the following hypotheses. H0: μ1 μ2 = 0 Ha: μ1 μ2 ≠ 0 The test statistic Z is computed to be 2.00. The p-value for this test is