2 Sample Hypothesis Testing Quiz

Formulate a null and alternative hypothesis for a 2 sample hypothesis test comparing the means of two independent groups.

• Alternative Hypothesis (H1): μ1 < μ2

• Null Hypothesis (H0): μ1 ≠ μ2

• Null Hypothesis (H0): μ1 > μ2

• { "Null Hypothesis (H0)": "μ1 = μ2", "Alternative Hypothesis (H1)": "μ1 ≠ μ2 (for a two-tailed test) or μ1 > μ2 (for a one-tailed test)" }

• Alternative Hypothesis (H1): μ1 = μ2

When should you use a t-test for 2 sample hypothesis testing?

• When comparing the means of two independent groups.

• When comparing the medians of two independent groups.

• When comparing the standard deviations of two independent groups.

• When comparing the proportions of two independent groups.

Calculate the test statistic for a 2 sample t-test given the sample means, sample standard deviations, and sample sizes of the two groups.

• t = (x1 - x2) / ((s1^2/n1) + (s2^2/n2)

• t = (x1 + x2) / √((s1^2/n1) + (s2^2/n2)

• t = (x1 - x2) / √((s1^2*n1) + (s2^2*n2)

• t = (x1 - x2) / √((s1^2/n1) + (s2^2/n2)

What does a p-value less than 0.05 indicate in the context of a 2 sample hypothesis test?

• The null hypothesis is rejected.

• The sample size is too small.

• The test is inconclusive.

• The alternative hypothesis is accepted.

Explain how you would draw a conclusion from the results of a 2 sample hypothesis test.

• Ignore the p-value and significance level and make a random conclusion

• Compare the p-value to the significance level to determine whether to reject or fail to reject the null hypothesis.

• Use the sample mean to determine the significance level

• Base the conclusion on the color of the pen used for the hypothesis test

Define Type I error in the context of 2 sample hypothesis testing and provide an example.

• Type I error is when we incorrectly conclude that there is no difference between two population means when there is actually a difference.

• In the context of 2 sample hypothesis testing, a Type I error would occur if we incorrectly conclude that there is a difference between two population means when there is actually no difference. For example, if we reject the null hypothesis that the mean heights of two populations are equal, when in reality they are equal.

• An example of a Type I error is concluding that there is no difference in the mean test scores of two groups, when in reality there is a difference.

• A Type I error occurs when we fail to reject the null hypothesis when there is actually a difference between two population means.

Define Type II error in the context of 2 sample hypothesis testing and provide an example.

• In the context of 2 sample hypothesis testing, a Type II error would occur if we fail to reject the null hypothesis that there is no difference in the mean scores between two groups, when in fact there is a difference.

• Type II error is only applicable in one sample hypothesis testing

• Type II error is the probability of correctly rejecting the null hypothesis

• Type II error occurs when we reject the null hypothesis when there is actually no difference between the two groups

Explain the consequences of committing a Type I error in a 2 sample hypothesis test.

• Falsely concluding that there is no difference between the two samples when there actually is

• Falsely concluding that the null hypothesis is true when it is actually false

• The consequence of committing a Type I error in a 2 sample hypothesis test is falsely concluding that there is a significant difference between the two samples when there isn't.

• Concluding that there is no significant difference between the two samples when there actually is

Explain the consequences of committing a Type II error in a 2 sample hypothesis test.

• The consequence of committing a Type II error in a 2 sample hypothesis test is the failure to detect a real difference or effect that exists in the population.

• Committing a Type II error leads to rejecting the null hypothesis when it is actually true

• The consequence of Type II error is the failure to reject the null hypothesis when it is actually false

• Type II error results in overestimating the effect size in the population

When would you use a one-tailed test in a 2 sample hypothesis test and how does it differ from a two-tailed test?

• A one-tailed test is appropriate for comparing means, while a two-tailed test is used for comparing proportions.

• A one-tailed test is used when the sample size is small, while a two-tailed test is used for large sample sizes.

• When you have a specific direction in mind for the difference between the two groups. A one-tailed test focuses on whether the difference is either greater or less than a certain value, while a two-tailed test looks for any difference between the two groups.

• In a one-tailed test, the null hypothesis is rejected if the p-value is less than 0.10, while in a two-tailed test, the null hypothesis is rejected if the p-value is less than 0.05.