Suppose that a study in a particular year showed that 43.5% of young drivers aged 16 -17 years old in a particular state admitted to texting while driving. Alarmed by this statistic, state law enforcement and local high-schools heavily promoted a social media campaign showing the dangers of texting and driving. Researchers then surveyed a random sample of 1017 teen drivers aged 16 17 years in the state and asked whether or not they had texted while driving in the previous month. They observed that 40% of the teen drivers surveyed admitted to texting while driving. Do the data provide evidence that 40% represents a significant decrease over the previous years statistic?

a. Write the hypothesis statements using words and symbols.

b. Use the appropriate applet to perform a test of significance on the observed statistic by simulating 1000 repetitions of this study. Obtain a p-value. Report the p-value and paste a screenshot of your applet here.

c. What is the center of your simulated null distribution and why does it make sense that this value is the center?

d. Describe exactly how the p-value is obtained from the 1000 simulated statistics. Dont just say that the applet does the work. Explain what work the applet is doing. If you had to find this pvalue by hand, how would you find it? Relate your answer to the definition of a p-value.

e. Suppose the researchers wanted to know if the observed statistic was different from the previous years without conjecturing a direction. How would the test of significance change?

f. Perform an appropriate test of significance using the alternative hypothesis that 40% is different than 43.5%. Describe exactly how the p-value is obtained using the distribution of sample statistics. Do you have evidence that 40% is a significant decrease? Report the p-value and paste a screenshot of your applet here.