Non-Calculus Based Probability and Statistics Test 3 Name: 1. Suppose the population standard deviation is = 5, an SRS of n = 100 is obtained, and the confidence level is chosen to be 98%. The margin of error. Find the margin of error. 2. Suppose the population standard deviation is = 5, an SRS of n = 100 is obtained, and the confidence level is chosen to be 99%. The margin of error for estimating a mean is given by 1.1650. To reduce the margin of error to 0.3883 you should change the sample size to what? 3. State the 4 steps for a hypothesis test. 4. State the 3 types of confidence intervals let us assume that 0 = 10. 5. State the 3 ways to get a smaller confidence interval. 6. A veterinarian collects data on the number of times race horses are raced during their career. The researcher finds the average number of races a horse enters is x = 15.3 with a standard deviation of s = 6.8 in a sample of n = 20 horses. (a) A 95% confidence for , the average number of times a horses races is what? (b) A rival researcher claims that the true population mean, , is 22. Preform a hypothesis test to test this claim. Page 2 7. A veterinarian does research on the causes of enteroliths, stones that develop in the colon of horses. She suspects that feeding alfalfa might be a cause. To investigate that suspicion, she selects five horses that are known to have enteroliths and compares the number of flakes of alfalfa they have eaten over a month with the number of flakes eaten by five horses free of enteroliths. The researcher found that for the enteroliths group has n=5, x = 45, and s=10. The healthy group had n=5, x = 28, and s=10. (a) Constuct a 95% confidence interval for the difference assume. Let enteroliths be group one and health be group 2 where the difference is group1-group2. (b) Preform a hypothesis test with = 0.05 8. What is the margin of error and what do you have to know to calculate it. Page 3 9. State a type I and a type II error. Which one is worse? 10. In the United States, there has historically been a strong relationship between smoking and education, with well-educated people less likely to smoke. To examine whether this pattern has changed, a sample of 459 men was selected at random from those who had visited a health center for a routine check-up over the course of the past year. Education is classified into three categories corresponding to the highest level of education achieved, and smoking status is classified into four categories. Education High School College Graduate Total Nonsmoker 56 37 53 146 Former 54 43 28 125 Moderate 41 27 36 104 Heavy 36 32 16 84 Total 187 139 133 459 (a) What is the proportion of former smokers with a university education (b) Suppose we wish to test the null hypothesis that there is no association between education level and smoking status. Under the null hypothesis, the expected number of nonsmokers with a high school education is what? (c) Preform a chi-square hypothesis test. Page 4 11. Two identical footballs, one air-filled and one helium-filled, were used outdoors on a windless day at the University of Tennessee's athletic complex, Neyland Stadium. Each football was kicked 10 times and the two footballs were alternated with each kick. The experimenter recorded the distance traveled by each ball in yards. Assume this is a random sample. (Note: MythBusters performed this experiment.) Air Helium Difference 25 21 23 16 19 25 16 13 35 28 15 22 26 29 24 29 24 22 27 28 (a) If you make a histogram of the difference with the information above can you use the t-distribution? Why or why not? (b) Conduct a hypothesis test to see if the distance traveled by the air-filled football is significantly less than the distance traveled by the helium-filled football at a 1% level of significances. Show all steps and interpret. Page 5