Math work

Written Homework # 5

I have attempted this assignment honestly and the material submitted is my own work. I have only worked with the other group members listed on this page. I have not copied from any source, and cited any materials I have used outside of lecture notes and the textbook.

Names: Signatures:

Chapter Objectives (ch 20, 21): Run a Hypothesis Test for a population proportion

Discuss Possible Errors in a Hypothesis Test Compute Power of a Test

Due Date: Monday, August 7

Statistics Summer 2017

1 Statistics show that since 2015, 171 of the 568 road deaths in Washington were blamed on some form of distracted driving. You believe that this proportion is higher in 2016 and you want to convince law-makers to pass stronger laws to combat this problem. You can’t find a compilation of all of the data, but you search through police records from around the state and find a sample of of 45 fatal accidents in 2016 and find that 18 of them were blamed on some sort of distracted driving.

Run a hypothesis test to decide if distracted driving-related fatalities increased from 2015 to 2016. Be sure to do the following:

(a) Decide an alpha-level for your test. Give reasons why you chose this.

(b) State the null and alternative hypotheses.

(c) Describe your model. Check that your data satisfies the assumptions and conditions necessary to proceed. What about this data set may not pass the conditions? How might you fix this? (After you note possible issues and possible solutions, suppose that they are not issues so that we can finish the hypothesis test.)

(d) Draw a picture of your model, shade the rejection region and plot your standardized test statistic.

(e) Report the p-value of your statistic, and make a decision about your null hypothesis.

(f) Compute a 90% confidence interval for the true proportion of distracted driving-related fatalities in 2016.

(g) Describe Type I and Type II errors and the possible social impact of making them associated with this test.

(h) Compute the power of this test and describe what this means.

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