MATH 3200 PROBABILITY AND STATISTICS M3200FL133.1

Size: px

Start display at page:

Download "MATH 3200 PROBABILITY AND STATISTICS M3200FL133.1"

Clarence Floyd
7 years ago
Views:

1 MATH 3200 PROBABILITY AND STATISTICS M3200FL133.1 In almost all problems, I have given the answers to four significant digits. If your answer is slightly different from one of mine, consider that to be roundoff error and mark the closely matching one. If your answer differs from the closest one of mine by more than one percent (meaning the ratio of yours to mine is less than 0.99 or greater than 1.01), then mark J) None of the. 1. Let p be the proportion of people in the population who prefer Gatorade over All Sport. Eighteen tasters participate in a taste-testing experiment, and twelve prefer Gatorade over All Sport. Suppose that a priori there is no reason to claim that one drink is preferred over the other. Therefore the alternative hypothesis is two-sided. What is the P-value? (Because of the small sample size, use an exact test, not a normal approximation.) A) B) C) D) E) F) G) H) I) J) None of the 2. A researcher desperate to find a statistically significant difference between two groups has data on 25 variables from each group. She tests 25 null hypotheses, each null hypothesis being that the group means are equal, hoping to find a significant difference on at least one variable. Suppose that the 25 tests are mutually independent and are conducted individually at the 5% level. What is the probability that at least one null hypothesis will be incorrectly rejected even if all null hypotheses are true? A) B) C) D) E) F) G) H) I) J) None of the

2 MATH 3200 PROBABILITY AND STATISTICS M3200FL An EPA researcher wants to design a study to estimate the mean lead level of fish in a lake located near an industrial area. Based on past sample data, the researcher estimates that σ for the lead level is mg/g. He wants to use a 95% CI having a margin of error no greater than mg/g. How many fish does he need to catch? A) 117 B) 128 C) 139 D) 150 E) 161 F) 172 G) 183 H) 194 I) 205 J) None of the 4. The mean ph value of a certain chemical is to be controlled at 5. Deviation from this target value in either direction is to be detected with high probability. For this purpose it is proposed to measure a certain number of samples from each batch and decide that the mean ph is different from 5 if the sample mean differs significantly from 5 at the 5% level of significance. What sample size is needed if the probability of not detecting a change of one standard deviation is to be no more than 1%? A) 13 B) 14 C) 15 D) 16 E) 17 F) 18 G) 19 H) 20 I) 21 J) None of the

3 MATH 3200 PROBABILITY AND STATISTICS M3200FL A random sample of size 12 is drawn from a normal population with μ = 70 and σ = 3. The mean of the sample is 6.45 and s = 5.2. Calculate a 95% t-interval for μ assuming you do not know σ, and report its length. A) B) C) D) E) F) G) H) I) J) None of the 6. In response to student complaints and financial considerations, a high school decides to close its kitchen and contract a food service to provide school lunches. The previous year, when food was prepared in the high school kitchen, 65% of the students purchased a lunch on a daily basis. The daily percentages of students using the food service during a two-week period are: 68% 61% 65% 74% 68% 90% 78% 63% 74% 85% The hypotheses are set up as H 0 : μ = 65% vs. H 1 : μ 65%. Calculate the P-value for the test. A) B) C) D) E) F) G) H) I) J) None of the

4 MATH 3200 PROBABILITY AND STATISTICS M3200FL The SAT scores (Mathematics plus Critical Reading plus Writing) for a freshman seminar class of 25 students at a private college averaged 2100 with a standard deviation s of 180. Assuming these students are a random sample of freshmen at that college, find a 95% prediction interval for the score of a future student. Subtract the lower limit of this interval from the upper limit to get the length of the interval and report that value. A) B) C) D) E) F) G) H) I) J) None of the 8. Tell in each of the following instances whether the study uses an independent samples ( I ) or a matched ( M ) design. a) Two computing algorithms are compared in terms of the CPU times required to do the same six test problems. b) A survey is conducted of teens from inner city schools and suburban schools to compare the proportion who have tried drugs. c) A psychologist measures the response times of subjects under two stimuli; each subject is observed under both stimuli in a random order. d) An agronomist compares the yields of three varieties of soybean by planting each variety in 10 separate fields of land, each one of which has been subdivided into three subplots, with the three varieties randomly allocated to the subplots within each field. abcd = : A) IIMM B) IMMM C) MMMM D) MIMM E) IIMI F) IMMI G) MIMI H) MIIM I) IIII J) None of the

5 MATH 3200 PROBABILITY AND STATISTICS M3200FL The effect of two types of virus on tobacco leaves was studied by rubbing a preparation containing each virus onto a different half of each of 8 tobacco leaves. The number of lesions counted on the two halves of these leaves were as follows: Tobacco Leaf Treated by virus Treated by virus Perform the appropriate Student s t-test on this data and report the two-sided P-value A) B) C) D) E) F) G) H) I) J) None of the 10. Two brands of water filters are to be compared in terms of the mean reduction in impurities measured in parts per million (ppm). A total of forty-five water samples were tested, and the reduction in the impurity level was measured, resulting in the following data: Filter 1: n l = 10 x = 8.8 s 1 2 = 9 Filter 2: n 2 = 35 ȳ = 5.9 s 2 2 = 4 Find the difference in degrees of freedom between the equal-variance t-test and the unequal-variance (Satterthwaite) t- test. A) B) C) D) E) F) G) H) I) J) None of the

6 MATH 3200 PROBABILITY AND STATISTICS M3200FL A restaurant adds a new commercial oven to its kitchen. It is hoped that the new oven has more evenly distributed heat than the current oven. The ovens are heated to 350 F, using a thermostat control, and temperature readings are obtained from thermometers placed at 12 locations in each oven, yielding the following data: Current oven: n l = 12 x = s 1 = 3.7 New oven: n 2 = 12 ȳ = s 2 = 2.1 Test H 0 : σ 1 = σ 2 vs. H 1 : σ l > σ 2. Report the one-sided P-value. A) B) C) D) E) F) G) H) I) J) None of the 12. While imprisoned by the Elbonians last year, Dilbert tossed a coin 5000 times and obtained 2567 heads. Perform a test of the null hypothesis that the coin was fair and report the two-sided P-value. Use a normal approximation without a continuity correction. A) B) C) D) E) F) G) H) I) J) None of the

7 MATH 3200 PROBABILITY AND STATISTICS M3200FL A blood test to identify patients at high risk of cardiac disease gave positive results on 15 out of 270 normal patients. Find the length of the 95% confidence interval for the specificity of the test. A) B) C) D) E) F) G) H) I) J) None of the 14. A study evaluated the urinary-thromboglobulin excretion in 12 normal and 12 diabetic patients. Summary results were obtained by coding values of 20 or less as low and values above 20 as high, as shown in the following table: Excretion Low High Normal 9 3 Diabetic 2 10 Perform a one-sided Fisher exact test to determine whether or not there is evidence for diabetics having a greater proportion of individuals with high excretion rates. Report the P-value of the test. A) B) C) D) E) F) G) H) I) J) None of the

8 MATH 3200 PROBABILITY AND STATISTICS M3200FL A genetics experiment on characteristics of tomato plants provided the following data on the numbers of offspring expressing four phenotypes. Phenotype Frequency Tall, cut-leaf 575 Dwarf, cut-leaf 180 Tall, potato-leaf 173 Dwarf, potato-leaf 58 Test the null hypotheses that theoretically the four phenotypes will appear in the proportion 9:3:3:1. Report the P-value of the test. A) B) C) D) E) F) G) H) I) J) None of the 16. Suppose that the Reader s Digest honesty experiment is modified to add a fifth city type, which we will call Rural. How many degrees of freedom does the chi-square test now have? A) 1 B) 2 C) 3 D) 4 E) 5 F) 6 G) 7 H) 8 I) 9 J) None of the

9 MATH 3200 PROBABILITY AND STATISTICS M3200FL The time between eruptions of Old Faithful geyser in Yellowstone National Park is random but is related to the duration of the last eruption. The table below shows these times for 5 consecutive eruptions. Duration of Last Eruption Time between Eruptions Find the slope of the least squares regression line predicting time between eruptions from duration of the last eruption. A) B) C) D) E) F) G) H) I) J) None of the 18. Using the data in Problem 17, calculate the length of a 95% prediction interval for the time between eruptions if the duration of the last eruption was 5 minutes. A) B) C) D) E) F) G) H) I) J) None of the

10 MATH 3200 PROBABILITY AND STATISTICS M3200FL Counts of the numbers of finger ridges for 6 pairs of siblings are given in the following table. Sibling Pair Sib 1 Ridge Count Sib 2 Ridge Count Calculate the 95% confidence interval for the correlation coefficient and report its length. A) B) C) D) E) F) G) H) I) J) None of the 20. A multiple linear regression model y = β 0 + β 1 x 1 + β 2 x 2 + β 3 x 3 is fitted to a set of 25 observations. The total sum of squares is SST = 164 and the error sum of squares is SSE = 130. Calculate the P-value for a test of the null hypothesis H 0 : β 1 = β 2 = β 3 = 0. A) B) C) D) E) F) G) H) I) J) None of the

Name: Date: Use the following to answer questions 3-4:

Name: Date: Use the following to answer questions 3-4: Name: Date: 1. Determine whether each of the following statements is true or false. A) The margin of error for a 95% confidence interval for the mean increases as the sample size increases. B) The margin