Statistics Quiz

When n=23, what is the degree of freedom?

• 22

• 23

• 24

• 25

Answer explanation

The degree of freedom is calculated as n - 1. When n = 23, the degree of freedom is 23 - 1 = 22. Therefore, the correct answer is 22.

What is the critical value when Ha: μ>µ0 and α=0.05?

• 0.4500

• 1.64

• 1.65

• 1.645

Answer explanation

The critical value for a one-tailed test with Ha: μ>µ0 at α=0.05 is found using the z-table. The z-score corresponding to 0.05 in the upper tail is 1.645, making it the correct choice.

Which of the following alternative hypotheses is illustrated by the graph above?

• Ha: µ>μ0

• Ha: µ≠μ0

• Ha: µ<μ0

• Ha: µ=μ0

Answer explanation

The graph indicates a right-tailed test, suggesting that the sample mean is greater than the hypothesized mean (μ0). Therefore, the correct alternative hypothesis is Ha: µ>μ0.

If the computed test statistic is 1.72. What decision can be made?

• Accept H0

• Accept H0 and Ha

• Reject Ha

• Reject H0

Answer explanation

A test statistic of 1.72 suggests that the null hypothesis (H0) is not supported by the data. Therefore, we reject H0, indicating that there is sufficient evidence to support the alternative hypothesis (Ha).

If the computed test statistic is 1.25. What decision can be made?

• Accept H0

• Accept H0 and Ha

• Reject Ha

• Reject H0

Answer explanation

A test statistic of 1.25 suggests that the evidence is not strong enough to reject the null hypothesis (H0). Therefore, we accept H0, indicating no significant effect or difference.

Which of the following serves a s the basis for either accepting or rejecting a hypothesis?

• Critical Value

• Degree of Freedom

• Significance Level

• z value

Answer explanation

The critical value is the threshold that determines whether to accept or reject a hypothesis based on the test statistic. If the test statistic exceeds the critical value, the null hypothesis is rejected.

What does α=0.05 mean?

• The rejection region has an area of 0.05.

• The rejection region has an area of 0.95.

• The acceptance region has an area of 0.05.

• The acceptance region has an area of 0.95.

Answer explanation

In hypothesis testing, α=0.05 indicates that the rejection region, where we would reject the null hypothesis, has an area of 0.05. This means there is a 5% risk of rejecting a true null hypothesis.

The computed test statistic falls within the rejection region, what decision can you make?

• Accept H0

• Accept H0 and Ha

• Reject Ha

• Reject H0

Answer explanation

When the computed test statistic falls within the rejection region, it indicates that the null hypothesis (H0) is unlikely to be true. Therefore, the correct decision is to reject H0.

What is referred to as the set of values of test statistic for which the null hypothesis is rejected?

• Critical Value

• Degree of Freedom

• Rejection Region

• Significance Level

Answer explanation

The rejection region is the set of values for the test statistic that leads to rejecting the null hypothesis. It is determined by the significance level and critical values, making it the correct choice.

The probability of rejecting the null hypothesis when it is true is called

• Critical Value

• Degree of Freedom

• Rejection Region

• Significance Level

Answer explanation

The significance level is the probability of rejecting the null hypothesis when it is true, often denoted as alpha (α). It defines the threshold for determining whether an observed effect is statistically significant.