Math Stats Exam Help

Multiple Choice For each of the following questions, choose the procedure from the following list that can be used to BEST answer the question asked. Note: some procedures may be used more than once!

(a) 1-sample z-test for population mean

(b) 1-sample z-Confidence Interval for population mean

(c) 1-sample t-test for population mean

(d) 1-sample t-Confidence Interval for population mean

(e) 2-sample t-test for a difference in population means

(f) 2-sample t-Confidence Interval a difference in population means

(g) 1-sample z-test for population proportion

(h) 1-sample z-Confidence Interval for population proportion

(i) 2-sample z-test for a difference in population proportion

(j) 2-sample z-Confidence Interval for a difference in population proportion

1. A high school randomly selected 200 students and asked them to estimate the amount of time they spent each week playing video games. The study found that the students played for 7.3 hours per week, on average, with standard deviation 1.1 hours. Estimate the true average amount of time high school students play video games.

2. A polling firm surveys 100 registered voters and finds that 62% of the participants agreed with the statement “I believe Obama has done a good job as President of the United States.” Does this survey give good evidence that a majority of Americans agree that Obama has done good job as President?

3. The University of Oregon investigated a possible difference in the proportions of male and female students who earned a passing grade in Math 111 between 2010 and 2015. In a random survey, 72 of 100 female students passed, while 65 of 150 male students passed. How large is the difference in passing rates between males and females?

4. Grades on a national physics exam are approximately Normally distributed, with standard deviation 12 points. The average score in an SRS of size 10 was 52 points. Evaluate the claim that the average score for the national exam is less than 60 points.

5. An advertising firm suspects that younger adults use social media more than adults over age 40. To see if this is true, they conducted a survey of 100 young adults and 101 adults over age 40. The young adults spent an average of 62 min- utes per day on social media, with standard deviation 5 minutes, while the adults over 40 spend an average of 55 minutes per day, with standard deviation of 10 minutes. Determine whether this survey supports the advertising firm’s suspicion.

Free-Response Problems (Write your answers clearly and concisely, including all work. If asked to explain something, use complete sentences. Any numerical answers may be written in approximate form as long an exact solving method is used.)

6. UrbanSpoon is a popular restaurant recommendation service freely available on Android, Windows, and iOS mobile devices. Users can participate in a simple “like” or “don’t like” ratings system to review restaurants. While browsing UrbanSpoon, you notice that the new Java the Hut coffee stand has received 8 positive “like” ratings, and 3 negative “don’t like” ratings. You are interested in determining the probability that a typical Eugene citizen would like the coffee stand, based on these reviews.

(a) What is the implied population and the sample in this survey?

(b) Explain why the conditions for using a large-sample confidence interval for population proportion are not satisfied in this situation.

(c) Estimate the probability that a randomly selected Eugene citizen would like the coffee stand, using a plus-four 90% confidence interval.

7. A new synthetic chemical has been developed that when added to drinking water, has the potential to eliminate the transmission of the deadly Malaria virus. However, implementing the treatment on a national level will cost billions of dollars. A comprehensive experiment is conducted to verify the effects of the treatment.

The chemical is secretly added to the water supply of 40 randomly selected small cities, while 60 small cities are selected as a comparative control. Researchers find that the average malaria rate for the 40 cities that received the chemical treatment was 0.5 cases per 10, 000 citizens (with standard deviation 1.8), while the average rate for the 60 cities that did not receive the treatment was 1.1 cases per 10, 000 citizens (with standard deviation 1.65).

(a) Does this experiment use a matched pair, or two-sample design? Explain your answer.

(b) Is there statistically significant evidence to suggest the drug is effective in reducing the transmission of malaria? In your answer, indicate which statistical procedure you choose, and verify that all conditions for its use are sufficiently satisfied.

8. A news station wants to conduct a survey to estimate the percentage of Oregon voters in favor of a bond to fund additional city library hours. Two years earlier, 45% of voters were in favor of a similar bond. Determine the sample size needed to be at least 99% confidant that the percentage obtained from the survey is within 2% of the true population percentage.

9. A stock investment firm is doing internal research, and wants to compare the performance of its East Coast and West Coast branches. Of 87 randomly selected stocks recommended by the East Coast branch, only 35 saw a net increase in value over a 1-month period. Meanwhile, 25 out of 73 random West Coast recommended stocks saw an increase in value. Determine whether there is evidence at the 10% level of a difference in performance between the two branches.