3.92 Better Traffic Flow. The dataset TrafficFlow gives delay time in seconds for 24 simulation runs in Dresden, Germany, comparing the current timed traffic light system on each run to a proposed flexible traffic light system in which lights communicate traffic flow information to neighboring lights. Since this is a matched pairs experiment, the variable Difference represents the time savings from the flexible system for each run of the simulation. We wish to estimate the average time savings for public transportation on this stretch of road if the city of Dresden moves to the new system. Set this up as a single mean because it comes from one quantitative variable (Difference). a. Define the parameter. b. Answer these questions to establish the process of generating one bootstrap sample: i. What sample size would you use for your bootstrap sample? ii. Would you sample with or without replacement? iii. What statistic would you record for this one bootstrap sample? Use correct notation: c. Use Statkey to find a 90% bootstrap confidence interval for the mean time savings, using percentiles. Use a few thousand samples. Include a screen shot showing the percentiles with your homework submission, and write the confidence interval here: d. Find a 95% bootstrap confidence interval using margin of error, based on the standard error estimate from your bootstrap distribution in the previous step (show all calculations). e. Interpret the 95% confidence interval in context. 2. The meaning of 95% confidence. Which of the following best explains the meaning of 95% confidence in the interval given in the last question? Check only one.  The population mean is in this interval 95% of the time  The population mean is believed to be in the interval. The methodology used to find this interval is correct 95% of the time.  There is a 95% chance that the sample mean from any random sample is in the interval. 3. 3.128 Who Smokes More: Male Students or Female Students? Data 1.1 includes lots of information on a sample of 362 college students. The complete dataset is available at StudentSurvey. We see that 27 of the 193 males in the sample smoke, while 16 of the 169 females in the sample smoke. We will investigate the difference in proportions of male and female students who smoke. a. Define the parameter(s). b. What is the best point estimate for the difference in the proportions of smokers? Use correct notation and include the value. c. Use Statkey to find a 99% bootstrap confidence interval using percentiles. Include a screen shot showing the percentiles, and write the confidence interval here: d. Find a 95% bootstrap confidence interval using margin of error, based on the standard error estimate from your bootstrap distribution in the previous step (show calculations). e. Refer to the 99% confidence interval. Is it plausible that the proportions of male and female students who smoke is the same? If so, how do you know? If not, which group is higher?

3.92 Better Traffic Flow. The dataset TrafficFlow gives delay time in seconds for 24 simulation runs in Dresden, Germany, comparing the current timed traffic light system on each run to a proposed flexible traffic light system in which lights communicate traffic flow information to neighboring lights. Since this is a matched pairs experiment, the variable Difference represents the time savings from the flexible system for each run of the simulation. We wish to estimate the average time savings for public transportation on this stretch of road if the city of Dresden moves to the new system. Set this up as a single mean because it comes from one quantitative variable (Difference).

a. Define the parameter.

b. Answer these questions to establish the process of generating one bootstrap sample:

i. What sample size would you use for your bootstrap sample?

ii. Would you sample with or without replacement?

iii. What statistic would you record for this one bootstrap sample? Use correct notation:

c. Use Statkey to find a 90% bootstrap confidence interval for the mean time savings, using percentiles. Use a few thousand samples. Include a screen shot showing the percentiles with your homework submission, and write the confidence interval here:

d. Find a 95% bootstrap confidence interval using margin of error, based on the standard error estimate from your bootstrap distribution in the previous step (show all calculations).

e. Interpret the 95% confidence interval in context.

2. The meaning of 95% confidence. Which of the following best explains the meaning of 95% confidence in the interval given in the last question? Check only one.

 The population mean is in this interval 95% of the time

 The population mean is believed to be in the interval. The methodology used to find this interval is correct 95% of the time.

 There is a 95% chance that the sample mean from any random sample is in the interval.

3. 3.128 Who Smokes More: Male Students or Female Students? Data 1.1 includes lots of information on a sample of 362 college students. The complete dataset is available at StudentSurvey. We see that 27 of the 193 males in the sample smoke, while 16 of the 169 females in the sample smoke. We will investigate the difference in proportions of male and female students who smoke.

a. Define the parameter(s).

b. What is the best point estimate for the difference in the proportions of smokers? Use correct notation and include the value.

c. Use Statkey to find a 99% bootstrap confidence interval using percentiles. Include a screen shot showing the percentiles, and write the confidence interval here:

d. Find a 95% bootstrap confidence interval using margin of error, based on the standard error estimate from your bootstrap distribution in the previous step (show calculations).

e. Refer to the 99% confidence interval. Is it plausible that the proportions of male and female students who smoke is the same? If so, how do you know? If not, which group is higher?