Math 140, Fa 13 Final Exam Pt II Name

Transcription

1 Math 140, Fa 13 Final Exam Pt II Name Show ALL work for full credit. Each problem, or part there-in, is 5 pts unless otherwise noted. The SPCA collect data on breed, age, weight, number of days housed, and veterinary costs for the dogs they house. 1) The veterinary bills for the dogs are summarized in the ogive below. Estimate the IQR of these expenses. 2) Which of the variables collected for only German Shepherds is most likely to be described by a Normal model? 3) Which data is categorical? 4) Costs for standard veterinary services at a local animal hospital follow a Normal model with a mean of $80 and a standard deviation of $20. a. Draw and clearly label this model. b. Is it unusual to have a veterinary bill for $125? Explain. c. What is the IQR for the costs of standard veterinary services? Show your work.

2 5) Sam is preparing sweet potato pies as his dessert for Thanksgiving. The store he shops at sells six sweet potatoes in a bag. He has found that each bag will contain 0, 1, or 2 bad sweet potatoes. Based on experience he estimates that there will be no bad sweet potatoes in 40% of the bags, one bad sweet potato in 30% of the bags, and two bad sweet potatoes in the rest. Conduct a simulation to estimate how many bags Sam will have to purchase to have three dozen sweet good potatoes. a. Describe how you will use a random number table to conduct this simulation. b. Show two trials by clearly labeling the random number table given below. Specify the outcome for each trial. c. State your conclusion. In an Intro Stats class, 57% of students eat breakfast in the morning and 80% of students floss their teeth. Forty-six percent of students eat breakfast and also floss their teeth. 6) What is the probability that a student from this class eats breakfast but does not floss their teeth? 7) Assume that 70% of teenagers who go to take the written drivers license test have studied for the test. Of those who study for the test, 95% pass; of those who do not study for the test, 60% pass. What is the probability that a teenager who passes the written drivers license test did not study for the test? (Hint: Create a table with these percentages applied to 100 students.)

3 8) The mean number of vacation days per year offered by different U.S. companies is skewed to the right. a. We collect data on the number of vacation days from a random sample of 60 companies across the United States. Why is it okay to use these data for inference even though the population is skewed? b. The mean and standard deviation of the 60 companies in our sample were 22 days and 9 days, respectively. Specify the sampling model (shape, center, spread) for the mean number of vacation days of such samples. c. Find a 95% confidence interval for the mean number of vacation days offered by U.S. companies. (i) (ii) (iii) d. Explain what 95% confidence means in this context.

4 9) Could eye color be a warning signal for hearing loss in patients suffering from meningitis? British researcher Helen Cullington recorded the eye color of 130 deaf patients, and noted whether the patient s deafness had developed following treatment for meningitis. Her data are summarized in the table below. Test an appropriate hypothesis and state your conclusion. (Hint: This is a goodness of fit test using the chi-squared model) (I) (II) (III) (IIV)

5 Answer Key Testname: STATFINALEXAMPT2ESSAY 1) $100 2) weight 3) breed 4) a. b. z = = 2.25, so the chance of being 2.25 standard deviations or more above average is = A 20 veterinary bill of $125 is unusual. c. Q1 has z = and Q3 has z = +0.67, so = y - 80 y = (20) = 66.6 and = y y = (20) = The IQR = Q3 - Q1 = = $ ) a. Use the digits 0-3 to represent bags with 6 good sweet potatoes (none bad), digits 4-6 to represent bags with five good sweet potato(one bad), and digits 7-9 to represent bags with four good sweet potatoes (two bad). Look at each single digit of the random number table to determine whether you have 4, 5, or 6 good sweet potatoes in the bag. Continue this until the cumulative count is at least 36 good sweet potatoes. b. Show two trials by clearly labeling the random number table given below. Specify the outcome for each trial. c. According to my simulation, it will take an average eight bags of sweet potatoes to get at least three dozen good sweet potatoes for the pies. 6) 11% 7) P(study) = 0.70, P(pass study) = 0.95, and P(pass did not study) = 0.60 P(pass) = P(pass study) P(study) + P(pass did not study) P(did not study) = (0.95)(0.70) + (0.60)(0.30) = P(did not study pass) = P(pass did not study) P(did not study) P(Pass) = (0.60)(0.30) = 0.213

6 Answer Key Testname: STATFINALEXAMPT2ESSAY 8) a. We have a large sample size. b. t 59!,! 60 c. Conditions: * Randomization condition: We have a random sample of U.S. companies. * 10% condition: The sample is less than 10% of the total number of U.S. companies. * Nearly Normal condition: We know the data is skewed, but we have a large enough sample size to proceed. We can find a t-interval for mean number of vacation days. We know: n = 60, y = 22, s = 9, and, SE(y ) = 9 60 = Our confidence interval has the form y ± t* n-1 t with 50 degrees of freedom). Our 95% confidence interval is then 22 ± = 22 ± 2.33, or 19.7 to s n. We have t* 59 = (we actually use the critical value for a We are 95% confident that the interval 19.7 to 24.3 contains the true mean number of vacation days that are given by U.S. companies. d. If many random samples of size 60 were taken, 95% of the confidence intervals produced would contain the actual mean number of vacation days offered by U.S. companies. 9) H0: Deafness and eye color are independent. HA: There is an association between deafness and eye color. These are counts of categorical data, assumed to be representative of deaf patients in Britain, with expected counts 25.1, 76.9, 6.9, and OK to do a chi-square test. df = 1,! 2 = 5.87, P = With P < 0.05, I reject the null hypothesis. There is strong evidence that hearing loss is associated with eye color. It appears that people with dark-colored eyes are at less risk of suffering deafness from meningitis.