Lab 5 and 6 Summer 2021 PDF

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Lab 5 and 6 work, for the summer semester of 2021...

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STAT 200 Lessons 5 & 6: Hypothesis Testing

Due Tuesday, June 15, 2021

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Answer the questions in this document in a different color and not bolded. Always show your work and clearly identify your final answer. Full credit will not be given to answers without work shown. If you do hand calculations, show your work using Word’s equation editor. When you use StatKey, include screenshots of all relevant output and clearly identify your final answer by writing a sentence (e.g., “The 95% confidence interval is…”). Round all answers to 3 decimal places unless otherwise specified. Copying answers from any source is an academic integrity violation. Posting content from this assignment to any online site outside of this course is an academic integrity violation. If you have any questions, post them to the course discussion board. Software needed: StatKey

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. There is one sample of people(American millennials) . We want to know if more than 30% have a tattoo. This is a single sample proportion test.

H0 :p = 0.3 Ha:p>0.3 Step 2: Construct a randomization distribution under the assumption that the null hypothesis is true. Take at least 5000 resamples.

STAT 200 Lessons 5 & 6: Hypothesis Testing

Due Tuesday, June 15, 2021

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

The p-value is 0.153

STAT 200 Lessons 5 & 6: Hypothesis Testing

Due Tuesday, June 15, 2021

Step 4: Decide if you should reject or fail to reject the null hypothesis. We should fail to reject the null hypothesis because the p value is greater than the alpha Step 5: State a real-world conclusion in relation to the original research question. There is not evidence that more than 30 percent of all American millennials have a tattoo. These results are not statistically significant

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. There is one sample of people(American millennials) . We want to know if more than 30% have a tattoo. This is a single sample proportion test.

H0 :p = 0.3 Ha:p>0.3 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.

STAT 200 Lessons 5 & 6: Hypothesis Testing

Due Tuesday, June 15, 2021

The p-value is 0.0058 Step 4: Decide if you should reject or fail to reject the null hypothesis. We should reject the null hypothesis because the p value is lesser than the alpha Step 5: State a real-world conclusion in relation to the original research question. There is evidence that more than 30 percent of all American millennials have a tattoo. These results are statistically significant

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? The P value is affected by sample size and the magnitude of the effect. The larger the sample size, the more likely a study will find a significant relationship if one exists. Hence why we saw a small p-value in part B than part A.

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

STAT 200 Lessons 5 & 6: Hypothesis Testing

Due Tuesday, June 15, 2021

comprehension scores than the current reading curriculum? This translates to the following hypotheses: H0: μnew = μcurrent Ha: μnew > μcurrent 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 in this specific scenario that in reality the new program is not improving the mean score but we wrongly infer it to be increasing it. B. What are the consequences of making a Type I error in this specific scenario? [5 points] There are many consequences of making this Type 1 error. The cost will increase and it will be an unnecessary burden. Teachers will also have to go through the hassle of learning the new material. And overall it will be a waste of time and effort for something which is ineffective. C. What does a Type II error mean in the specific scenario? [5 points] A Type II error would occur if the new curriculum is improving the mean scores but we wrongly infer that it does not improve the scores. D. What are the consequences of making a Type II error in this specific scenario? [5 points] The students would miss out at an opportunity for a better version of the curriculum. This in turn would cost the image of the school and impact their reputation. E. In this scenario, is a Type I or Type II error more serious? Or, are they equally serious? Explain your reasoning. [10 points] I think type 1 would be more serious as there are higher costs incurred compared to the type 2 error. Both cost and time are being jeopardized in type 1 error. 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] I would choose alpha= 5 percent because that would be considered as we would be 95 percent sure that we are taking the right decision....