1. Inference Review Game
Created by Educational Technology Network

2. POWERPOINT JEOPARDY
Category 1
Category 2
Category 3
Category 4
Category 5 10 10 10 10 10 20 20 20 20 20 30 30 30 30 30 40 40 40 40 40 50 50 50 50 50

3. Two Polish math professors and their students spun a Belgian euro coin 250 times. It landed on heads 140 times. One of the professors concluded that the coin was minted asymmetrically. A representative from the Belgian mint said that the result was just by chance. Is the math professor or the representative from the Belgian mint correct? Calculate the appropriate p-value for this scenario.

4. Let’s say that 58% of 462 randomly selected college freshman (from colleges across the nation) reported being overwhelmed by the task of managing their time. Construct and interpret a 90% confidence interval for the true proportion of college freshman that are overwhelmed by the task of managing their time.

5. According to one source, newborn baby weights have a mean of 7
According to one source, newborn baby weights have a mean of 7.5 pounds with a standard deviation of 1.1 pounds. If these numbers are accurate, what proportion of samples of n=50 would have a sample mean greater than 8 pounds?

6. Mrs. Johnson wants to know how many hours per week senior students spend with their friends in person (not texting, snapchatting, on the phone, etc.). How many senior students must be randomly selected if she wants a 95% confidence level with a standard error of no more than 1.5 hours, assuming she somehow knows the population standard deviation will be 4 hours.

7. Do males and females differ in their test scores for exam 2
Do males and females differ in their test scores for exam 2? The mean test score for females is 27.1 (s=2.57, n=19), and the mean test score for males is 26.7 (s=3.63, n=20) Calculate the margin of error for a 98% confidence interval.

8. A psychologist finds that fidgety patients tap their fingers on average 500 times during a 2 hour period. They wish to test if this is still true for the same patients, but in a room decorated with soothing colors and soft lighting. They believe that a warmly decorated room may alter the fidgeting behavior, causing subjects to tap their fingers less than they do under normal conditions. A random sample of 400 patients has a mean of 420 taps and a standard deviation of 60 taps in a 2 hour period. Does this show a statistically significant difference?

9. Suppose that simple random samples of college freshman are selected from two universities - 15 students from school A and 20 students from school B. On a standardized test, the sample from school A has an average score of 1000 with a standard deviation of 100. The sample from school B has an average score of 950 with a standard deviation of 90. Describe the Distribution

10. Clinic reports 43 live births to 151 women under 38, 6 out of 81 for women 38 and older. Let p1 be the proportion for women under 38, p2 for 38 and older. What is the probability that there is a difference greater than 30%?

11. The Centers for Disease Control report a survey of randomly chosen Americans age 45 and older, which found that 51 of 100 men and 80 of 782 women suffered from some form of arthritis. You want to estimate the difference in the proportions of men and women over 45 who have arthritis with a 95% confidence interval. What standard error will you use?

12. Is there sufficient evidence to suggest improvement?
A fitness trainer wants to know if her weight-lifting program can quickly improve upper body strength in older people. To find out, she has a group of randomly selected people over 55 years old do push-ups for 90 seconds and counts the number each can do. After these people participate in her weightlifting program for 3 weeks, she tests them again in the same way. Here are the results:
Is there sufficient evidence to suggest improvement?

13. By Increasing the sample size, the margin of error becomes ___________(larger/smaller) and the length of the confidence interval ___________ (widens/narrows).

14. There's one high school in particular that believes that their students scored significantly better than the state average . So in order to test their hypothesis, they took a random sample of 15 students' scores. They calculated the t-score for us, and have plotted it on a t-distribution. So we have a t score of Find the p-value.

15. Milligrams of tar per cigarette
Cigarettes. Some of the cigarettes sold in the US claim to be “low tar”. How much less tar would a smoker get by smoking low tar brands instead of regular cigarettes? Samples of 15 brands of each type were randomly selected from the 1206 varieties (no kidding) that are marketed. Their tar contents (mg/cig) are listed in the table below. Find a 95% confidence interval for the difference between regular and low tar brands.
Type
Milligrams of tar per cigarette
Regular 18 10 14 15 12 17 11
Low Tar 9 5 4 8 3 7 6

16. A research team is interested in the difference between serum uric acid levels in patients with and without Down's syndrome.  In a large hospital for the treatment of the mentally retarded, a sample of 12 individuals with Down's syndrome yielded a mean of   = 4.5 mg/100 ml.  In a general hospital a sample of 15 normal individuals of the same age and sex were found to have a mean value of = 3.4 mg/100 ml.  If it is reasonable to assume that the two populations of values are normally distributed with variances equal to 1 and 1.5, find the margin of Error.

17. An agronomist hopes that a new fertilizer she has developed will enable grape growers to increase the yield of each grapevine by more than 5 pounds. To test this fertilizer she applied it to 44 vines and used traditional growing strategies on 47 other vines. The fertilized vines produced a mean of 58.4 pounds of grapes with a standard deviation of 3.7 pounds, while the unfertilized vines yielded an average of 52.1 pounds with standard deviation of 3.4 pounds of grapes. Do these experimental results confirm the agronomist’s expectations?

18. Waiters are expected to keep track of their income from tips and report it on their income tax forms. The Internal Revenue Service suspects that one waiter (we’ll call him “Jared”) has been under-reporting his income, so they are auditing his tax return. An IRS agent goes through the restaurant’s files and obtains a random sample of 80 credit card receipts from people Jared served. The average tip size shown on these receipts was $9.68 with a standard deviation of $2.72.
Create and interpret a 90% confidence interval for the mean size of all of Jared’s credit card tips.

19. You are going to create a 95% confidence interval for a population proportion and want the margin of error to be no more than Historically, data indicated that the population proportion has remained constant at about What is the minimum sample size you need to construct this interval?

20. The data below give the mercury content of randomly selected fish in the lakes of Maine.
Is there sufficient evidence to suggest there is a difference in the average mercury between lakes formed by dams and naturally formed lakes?

21. A survey of 430 randomly selected chosen adults found that 21% of 222 men and 18% of 208 women had purchased books online.
Is there evidence that men are more likely than women to make online purchases of books? Test an appropriate hypothesis and state your conclusion in context.

22. A study of the survival of small businesses chose a random sample from the telephone directory’s Yellow Pages listings. Interviews were completed with 148 businesses; 106 were headed by men and 42 by women. Three years later, 22 of those businesses had failed: 15 headed by men, 7 by women. Calculate the margin of error.

23. Consumer Reports gave the following information about annual premiums (in dollars) for all insurance companies for renewable life insurance policies with similar benefits:
Find a 90% confidence interval for the average of all annual premiums for such life insurance policies.

24. The EPA reports that the exhaust emissions for a certain car model has a normal distribution with a mean of 1.45 grams of nitrous oxide per mile and a standard deviation of 0.4. The car manufacturer claims their new process reduces the mean level of exhaust emitted for this car model. A SRS of 28 cars is taken and the mean level of exhaust emitted for this sample is 1.21 grams.

25. Fatty acids present in fish oil may be useful for treating some psychiatric disorders. An article reported September 3, 1998 at the Yahoo Health website described a randomized experiment done by a Harvard Medical School researcher in which 14 bipolar patients received fish oil daily, while 16 other patients received a placebo daily. After four months, 9 of the 14 patients who received fish oil had responded favorably, but only 3 of the 16 placebo patients had done so. Calculate and interpret a 90% confidence interval for the difference between the proportions showing favorable response in the two groups

26. Has retention rate at WMU been changing
Has retention rate at WMU been changing? Suppose that a random sample of 200 entering students in 1989 showed 74% were still enrolled 3 years later. Another random sample of 200 entering students in 1999 showed that 66% were still enrolled 3 years later. This constitutes an 8% change in 3-year retention rate. However, the 8% difference is based on random sampling, and is only an estimate of the true difference. What is the likely size of the error of estimation?

27. A group of 12 companies in the insurance industry has a mean annual profit as percent of revenue of 4.4 with a standard deviation of 1.6 while the mean annual profit as a percent of revenue for a group of 10 health care companies was 4.6 with a standard deviation of Calculate the margin of error.