Q: A researcher wants to estimate the mean score of students who received reminders. The sample mean is 75.42, the sample standard deviation is 10.98, and the sample size is 30. What is the 95% confidence interval for the mean?

$$75.42 \pm 2.04 \times \frac{10.98}{\sqrt{30}}$$

Question 1

Suppose Bay Ridge is looking to improve student engagement with online homework. They randomly assign students to two groups: one receives reminders, the other does not. Which statistical test is most appropriate to compare the mean homework completion rates between the two groups?

Accepted Answer

A two-sample t-test

Question 2

A researcher wants to estimate the mean score of students who received reminders. The sample mean is 75.42, the sample standard deviation is 10.98, and the sample size is 30. What is the 95% confidence interval for the mean?

Accepted Answer

$$75.42 \pm 2.04 	imes \frac{10.98}{\sqrt{30}}$$

Question 3

Which of the following best describes the null hypothesis for comparing the mean homework completion rates between students who received reminders and those who did not?

Accepted Answer

The mean completion rates are equal for both groups.

Question 4

If the p-value for the two-sample t-test comparing reminder and no-reminder groups is 0.03, what is the correct interpretation at the 0.05 significance level?

Accepted Answer

There is enough evidence to reject the null hypothesis.

Question 5

A student calculates the standard error for the mean using the formula $$SE = \frac{s}{\sqrt{n}}. If$$ $$s = 10.98$$ and $$n = 30$$, what is the value of the standard error?

Accepted Answer

$$SE = \frac{10.98}{\sqrt{30}} = 2.004$$

Question 6

Which of the following is a plausible reason for using a two-sample t-test instead of a paired t-test in the Bay Ridge study?

Accepted Answer

The two groups are independent and not matched.

Question 7

A student wants to test if reminders increase homework completion. Which is the correct alternative hypothesis?

Accepted Answer

$$\mu_{reminder} \u003e \mu_{no-reminder}$$

Question 8

If the confidence interval for the difference in means between reminder and no-reminder groups is $$[2.1, 7.3]$$, what does this imply?

Accepted Answer

The reminder group has a significantly higher mean completion rate.

Question 9

Which formula is used to calculate the t-statistic for comparing two independent means?

Accepted Answer

$$t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}}$$

Question 10

A student finds a p-value of 0.07 for the difference in means. What should they conclude at the 0.05 significance level?

Accepted Answer

Fail to reject the null hypothesis.

Question 11

Which of the following is NOT an assumption of the two-sample t-test?

Accepted Answer

The data is categorical.

Question 12

If the sample sizes for the two groups are unequal, which formula should be used for the standard error in the two-sample t-test?

Accepted Answer

$$SE = \sqrt{\frac{s_1$^2}{n_1$} + \frac{s_2$^2}{n_2$}}$$

Question 13

A student wants to check if the difference in means is statistically significant. Which value should they compare the t-statistic to?

Accepted Answer

The critical value from the t-distribution with appropriate degrees of freedom.

Question 14

If the confidence interval for the mean completion rate in the reminder group is $$[72.5, 78.3]$$, what does this interval represent?

Accepted Answer

The range of values likely to contain the true mean completion rate.

Question 15

Which scenario would require a paired t-test instead of a two-sample t-test?

Accepted Answer

Comparing pre- and post-intervention scores for the same students.

Question 16

A student calculates a 95% confidence interval for the mean as $$[70.2, 80.6]. $$What is the correct interpretation?

Accepted Answer

We are 95% confident that the true mean lies between 70.2 and 80.6.

Question 17

Which of the following would increase the width of a confidence interval for the mean?

Accepted Answer

Increasing the standard deviation.

Question 18

If a student incorrectly uses a one-sample t-test instead of a two-sample t-test for comparing two groups, what is a likely consequence?

Accepted Answer

The results may be invalid due to incorrect assumptions.

Question 19

Which formula is used to calculate the margin of error for a confidence interval for the mean?

Accepted Answer

$$ME = t^* 	imes \frac{s}{\sqrt{n}}$$

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