Use 3 decimal places where applicable

Please solve the problems by yourself instead of using AI.

1. A statistics instructor is designing a finalexam and wonders how many questions to ask on the exam. The exam is scheduled for two hours. Imagine that each question takes the exact same amount of time to completeand based on a sample of 81 students the mean number of minutes needed to complete one question is 14.5 minutes with a standard deviation (s) of 4.5 minutes.

1. 5 points.Construct a 95% confidence interval for the population mean time to complete one problem and interpret the meaning of the interval that you compute.

1. 1 point. Based on this information, is it a good idea for the instructor to include eight problems on the exam if the instructor wants to be nearly 100% certain (this certainty does not imply a confidence interval) that well over half of the students will complete the exam. Why or why not? (Can be answered in no more than two or three sentences.)

1. 2 points.If the time to completeoneproblem is Normally distributed, what proportion of the class is likely to take more than 15 minutes to completea problem if the true population mean () is 14.2 minutes and the true population standard deviation () is 3.4 minutes.
2. A researcher wants to know how much time the average 11^thgrader is spending on social media in one day. A random sample of 576 11^thgraders is collected and the sample mean is 76.278 minutes with a standard deviation of 80 minutes.

1. 5 points. Construct a 99% confidence interval for the population mean of social media usage per day among 11^thgraders.

1. 1 point. If we were to compute a 75% confidence interval, would this interval be wider than the interval computed above (meaning the margin of error is larger in a 75% confidence interval compared with a 99% confidence interval)? Why or why not? (Note that the t-table does not provide a way to directly compute a 75% confidence interval.)

1. Extra Credit 1 point. What distribution shape (symmetric, skewed right or skewed left) of thesampledistribution (not population or sampling) is by far the LEAST likely and why did you choose that shape?

3. 18 pointsIs there a relationship between race/ethnicity and whether or not one has tried alcohol among teenage girls. Using data found in the 2008Monitoring the Futurestudy, conduct a chi-square test to examine the potential relationship between these variables. Use = .05.

		Race
Ever tried alcohol?	White	Black	Hispanic
No	121	37	22
Yes	315	57	69

4. 18 points.A researcher believes that perceptions about violent crime are related to the type of community where one was raised (rural, suburban, urban). A sample of 400 individuals is taken and it is found that 40% of the sample are from rural background, 42.5% are from a suburban background and 17.5% are from an urban background.

1. Among those from an urban background, 14.286% believe violent crime is a significant and growing problem; 42.857% believe it is important, but controlled; and 42.857% believe it is not significant.
2. Among those from a suburban background, 17.647% believe that violent crime is a significant and growing problem; 47.059% believe it is important, but controlled; and 35.294% believe that is not a significant problem.
3. Finally, among those from a rural background, 6.25% believe violent crime is a significant and growing problem; 56.25% believe that is an important problem, but largely controlled; and 37.5% believe that is not a significant problem.

Based on this data, does it seem likely that there is a relationship between perceptions of violent crime and community background.Conduct a chi-square test to examine the potential relationship between these variableswith an = .01

		Violent Crime Perception
Community Background	Significant + Growing	Important, but Controlled	Not significant
Urban	10	30	30	70
Suburban	30	80	60	170
Rural	10	90	60	160
	50	200	150	400