Background: A large city’s department of education operates public high schools at locations throughout the city. Traditionally the schools have scheduled their classes in 1-hour sessions offered each day. The leaders of the department of education are considering a change in this schedule. Some classes could be shifted to 2-hour sessions offered every other day. There are also possibilities to partially implement this schedule (e.g. in mornings only or in afternoons only). The possible schedules are shown below:

- A: 1-Hour Sessions (All Classes)
- B: 1-Hour Sessions (Morning), 2-Hour Sessions (Afternoon)
- C: 2-Hour Sessions (Morning), 1-Hour Sessions (Afternoon)
- D: 2-Hour Sessions (All Classes)

This change could have many potential effects. For this investigation, the department of education wants to focus on the experience of teachers who work with these different schedules. The planned study will have the following characteristics:

- The public schools will be randomly divided into 4 groups (A, B, C, and D). Each school will be assigned the corresponding class schedule listed above for the next school year.
- The department of education has hired an outside firm to conduct a survey of the teachers. The firm will send the teachers an e-mail with a link to the survey. Each teacher will have the opportunity to respond to the survey anonymously. Each teacher may voluntarily choose to participate or not participate. There will be no consequences for choosing not to participate.

1.The length of the survey is

a.Too long because no one has time to answer this number of questions.

b.Too short because there are many more important aspects of the teaching experience that are not covered at all.

c.About the right length because the teachers can answer these questions in a reasonable amount of time.

d.Not an important consideration since we’ll gather data from those teachers who decide it’s important enough to participate.

2.Teachers will surely be more likely to participate in the survey if they

a.Have strong opinions about the scheduling changes.

b.Do not have strong opinions about the scheduling changes.

c.Fear the repercussions of sharing their opinions about the scheduling changes.

d.Are teachers of a foreign language.

3.The teachers who participate will have an incentive to

a.Lie about their experiences because they don’t want to look like they are complaining about the changing schedule.

b.Lie about their experiences because they wouldn’t want to look like they are performing poorly as teachers.

c.Tell the truth about their experiences because they want to demonstrate that they are performing well as teachers.

d.Tell the truth about their experiences because they have an interest in the scheduling decisions and appreciate being able to provide input.

4.Let’s consider the following two statements from the survey:

Q1: I am satisfied with my teaching schedule.

Q9: I would prefer teaching in 2-hour sessions instead of 1-hour sessions.

Which of these statements would better inform the department of education’s choices for this study?

a.Q1 is more relevant than Q9 because satisfaction is the best way to measure whether the change in schedule benefits the teachers.

b.Q1 is more relevant than Q9 because it is a more holistic measurement of the teaching experience.

c.Q9 is more relevant than Q1 because it directly asks the teachers to state a preference on this decision.

d.Q9 is more relevant than Q1 because it gives more of a voice to dissatisfied teachers.

5.Collecting data from a large sample size in each group (A, B, C, D) using the study’s methods will…

a.Ensure that we have a representative sample from the population.

b.Ensure that the groups are all balanced in terms of other factors (e.g. demographics).

c.Fully isolate the effect of the scheduling changes on the average satisfaction score from Q1 of the survey for the full population.

d.Allow for comparisons of the groups that are subject to limitations around participation and the survey’s design.

6.The preferred statistical method for comparing the average satisfaction scores (from the survey’s Q1) of the groups would be:

a.A two-sample, one-sided t test.

b.A two-sample, two-sided test of proportions.

c.Logistic Regression.

d.Linear Regression or ANOVA.

7.Suppose that we are focusing only on the comparison between group A (all 1-hour sessions) and group D (all 2-hour sessions). The leaders of the department of education think the shift to 2-hour sessions should lead to a 0.5 point increase in the average satisfaction score (Q1 of the survey). Let’s suppose that we can obtain 100 responses in each group, the standard deviation of the satisfaction score is 2, and that we’re using a 0.05 significance level for the statistical test. What would be the statistical power for this test? Round your answer to 3 decimal places.( please give me the calculation process)

- Using the information from the prior question, what would happen if the data’s standard deviation were lower than the value of 2 we assumed?

a.The reduced standard deviation would lead to an increased effect size, so the statistical power would increase.

b.The reduced standard deviation would lead to an increased effect size, so the statistical power would decrease.

c.The reduced standard deviation would lead to an decreased effect size, so the statistical power would increase.

d.The reduced standard deviation would lead to an decreased effect size, so the statistical power would decrease.

9.Using the setting of the prior two questions, what is the minimum sample size we would need in each group to demonstrate that switching fully to 2-hour sessions (group D) would increase the average satisfaction score (Q1) of teachers by 0.5 points relative to the traditional schedule (group A)? Assume a standard deviation of 2, a significance level of 0.05, and a statistical power of 0.8. Make sure that your answer is the sample size per group, not the sum for the two groups. please give me the calculation process.

10.Relative to the previous question, if the real increase in the average satisfaction score is smaller than 0.5, then the required sample size would

a.Decrease because it is easier to demonstrate a smaller effect than a larger one.

b.Increase because it is more difficult to demonstrate a smaller effect than a larger one.

c.Stay the same because the decrease in the effect size would be offset by an increase in the standard error.

d.Not be a relevant concern because we can never tell if rejecting the null hypothesis is a false positive or a true positive.

11.Now consider a comparison of all four groups (A, B, C, D) in terms of their average preference for 2-hour sessions (Q9 on the survey). We would like to detect a moderate effect size (f = 0.2) with a significance level of 0.05. Assuming balanced sample sizes, what is the minimum number of respondents needed in each group to reach a statistical power of 0.75? (Do not add the sample sizes for the four groups.) please give me the calculation process.

- Schedules B and C mix 2-hour and 1-hour sessions together. Operationally speaking, this may:

(Select all that apply.)

a.Not allow the teachers to fully evaluate the shift to the new schedule when they respond to the survey.

b.Create difficulties for the teachers and students in shifting between the schedules.

c.Not be measurable in terms of the data and the statistical tests.

d.Require more significant training as the teachers have to prepare in both the old and new scheduling formats.

13.So far we have assumed that the randomized assignment of schedules will allow us to use the standard statistical tests and models for the analyses. Which of the following possible limitations might lead to reconsidering our approach?

(Select all that apply.)

a.Randomizing the schedules by school could mean that the teachers within a single school would have some correlation in their responses.

b.For teachers assigned to schedules that mix 1-hour and 2-hour sessions (Groups B and C), the difficulty of shifting back and forth may detract from any benefit that a 2-hour class schedule might provide.

c.We are only conducting the study within one city. It doesn’t tell us anything about the effect of the scheduling changes on the teaching experience in other cities.

d.We are only conducting the study within public schools, so it doesn’t tell us anything about the effect on the teaching experience in private schools.

14.Select any quantitative question from the survey (Q1 through Q9). For that question, state and justify an opinion about the possible effect size that would result from shifting fully to 2-hour teaching sessions (Group D) relative to traditional classes in 1-hour sessions (Group A). Describe whether and how this change would be meaningful for the teachers.

- What other changes could the department of education consider to improve the experience of the teachers? Describe your proposed change. Then pick one quantitative survey question (Q1 through Q9) and describe what kind of improvement you think this change would produce in the average scores.

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