Question Set 1. Millennials & Tattoos

In this question set you will use StatKey to conduct two different randomization tests. These data are not built in to StatKey, so you will need to "Edit Data" to manually enter them. For each part of this question set, use the following research question: Do more than 30% of all American Millennials have a tattoo?

A. In a random sample of 30 Millennials, 11 said they had a tattoo. Using the five steps from the online notes, conduct a randomization test to address the research question above. Be sure to include your relevant StatKey output. [25 points]

Step 1: Determine what type of test you need to conduct and write the hypotheses.

Step 2: Construct a randomization distribution under the assumption that the null hypothesis is true. Take at least 5000 resamples.

Step 3: Use the randomization distribution to find the p-value.

Step 4: Decide if you should reject or fail to reject the null hypothesis.

Step 5: State a real-world conclusion in relation to the original research question.

B. In a random sample of 300 Millennials, 110 said they had a tattoo. Using the five steps from the online notes, conduct a randomization test to address the research question above. Be sure to include your relevant StatKey output. [25 points]

Step 1: Determine what type of test you need to conduct and write the hypotheses.

Step 2: Construct a randomization distribution under the assumption that the null hypothesis is true. Take at least 5000 resamples.

Step 3: Use the randomization distribution to find the p-value.

Step 4: Decide if you should reject or fail to reject the null hypothesis.

Step 5: State a real-world conclusion in relation to the original research question.

C. Compare your results from parts A and B. The hypotheses and sample proportions should have been the same in each part. Explain why the p value decreased when the sample size increased. [10 points]

Hint: Compare the two randomization distributions. How did they change? How did that impact the p value?

Question Set 2. Comparing Curricula

An elementary school is considering changing their reading curriculum. They plan to conduct a randomized experiment with a sample of 38 students to address the following research question: Does the new reading curriculum produce higher reading comprehension scores than the current reading curriculum? This translates to the following hypotheses:

H₀: _new = _current

H_a: _new > _current

The new curriculum is slightly more expensive than the current curriculum. And, in addition to the cost of the curricular materials, all elementary school teachers and instructional support staff would need to be trained on how to use the new materials if the decision is made to change curricula.

A. What does a Type I error mean in the specific scenario? [5 points]

A Type I error would occur if...

B. What are the consequences of making a Type I error in this specific scenario? [5 points]

C. What does a Type II error mean in the specific scenario? [5 points]

A Type II error would occur if...

D. What are the consequences of making a Type II error in this specific scenario? [5 points]

E. In this scenario, is a Type I or Type II error more serious? Or, are they equally serious?Explain your reasoning. [10 points]

F. If you were working with this school district, what alpha level would you use for this research study? Explain your reasoning. Your answer should be consistent with your argument in part E. [10 points]