Reference no: EM133371511
1. In a sample of 20 marijuana users, the mean number of prior emergency room admissions was 1.8 with a standard deviation of 0.5. Construct a 95% confidence interval for the population mean number of emergency room admissions and interpret your results.
2. We take a sample of 142 gun owners in Prince George's county and ask them how many days in a month they carry a gun on their person. The sample mean is 2.3, with a standard deviation of 1.1. Construct a 92% confidence interval around the sample mean and interpret it. What would happen to our confidence interval if it we increased our confidence level from 91% to 96%? Why?
What would happen to our confidence interval if we increased our sample size to 1000? Why?
3. A candidate running for mayor of your city wants to propose a new policy which allows for needle exchange for drug addicts. She is not sure, however, how the public feels about this so she hires you to carry out a poll to see what people want. You poll 400 people and find that 52% support her idea for a needle exchange program.
a. Construct a 93% confidence interval around this proportion and interpret it.
b. Since she was trailing in the polls, would you have advised her to propose her plan? Why or why not?
4. According to the US Chamber of Commerce, the annual average loss due to employee theft is $775 per employee. Take this as your population value. You take a random sample of 200 companies that are owned by their employees and find that the mean loss due to employee theft for these employee-owned companies is $745 with a standard deviation of $200. Test the null hypothesis that the real population value of average theft for employee-owned companies is $775, against the alternative that it is less than that. Use an alpha level of 0.02. State each step of your hypothesis test. Interpret your results.
5. A criminology professor wants to estimate the population mean performance for her current class of 25 students. The average this semester was 84 with a standard deviation of 12.6. In the past 20 semesters that the professor has taught this class, the average performance in the class was a 78.5. Test the null hypothesis that the current class is the same as the previous classes against the alternative hypothesis that this current semester has students who are genuinely smarter. What do you conclude? Use an alpha level of 0.01. State each step in your hypothesis test.
6. You want to estimate the proportion of kids between the ages of 12 and 15 who have tried marijuana. You take a random sample of 130 Maryland students and find that 21% of the sample report having tried marijuana. Last year, the federal government ran a much larger survey of 10,000 students and found that 27% reported ever using marijuana. Test the null hypothesis that the true population proportion of Maryland students who have smoked marijuana is 27% versus the alternative hypothesis that it is different than that. Use a 3% significance level. Interpret your result.
Without calculations - if you were to make a 97% confidence interval around your sample proportion of .23, would your population proportion of .29 be contained in the interval.