Statistics Exam Answer Key

STATISTICS SECTION II Part A Questions 1-5 Spend about 65 minutes on this part of the exam. Percent of Section II score-75 Directions: Show all your work. Indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. 1. An environmental group conducted a study to determine whether crows in a certain region were ingesting food containing unhealthy levels of lead. A biologist classified lead levels greater than 6.0 parts per million (ppm) as unhealthy. The lead levels of a random sample of 23 crows in the region were measured and recorded. The data are shown in the stemplot below. Lead Levels 28 30 3588 4112 4688 5012234 599 634 668 Key: 2/8 2.8 ppm 4 23 1739 (a) What proportion of crows in the sample had lead levels that are classified by the biologist as unhealthy? X= (b) The mean lead level of the 23 crows in the sample was 4.90 ppin and the standard deviation was 1.12 ppm. Construct and interpret a 95 percent confidence interval for the mean lead level of crows in the region. 5= 22 4.90± (2.074) 1.12 √23 (4.4157, 5.3843) SRS stemplot is approx symm no outllers or strong skew We are 95% confident that the twe mean lead level of crows. in the region is b/w 4.4157 & 5.3843 ppm. -6- GO ON TO THE NEXT PAGE. 2. An administrator at a large university wants to conduct a survey to estimate the proportion of students who are satisfied with the appearance of the university buildings and grounds. The administrator is considering Three methods of obtaining a sample of 500 students from the 70,000) students at the university. Student's who are first to attend might think the grounds are in grent condition, so proportion of satisfied students. ore likely to overestimate the tre propor. they mere (a) Because of financial constraints, the first method the administrator is considering consists of taking a convenience sample to keep the expenses low. A very large number of students will attend the first football game of the season, and the first 500 students who enter the football stadium could be used as a sample. Why might such a sampling method be biased in producing an estimate of the proportion of students who are satisfied with the appearance of the buildings and grounds? Number students 00001 to 70000 alphabetically. Randomly ure the first 500 #'s chosen. to select the sample. Igmre repeats & numbers not in the range. Because of the large number of students at the university, the second method the administrator is considering consists of using a computer with a random number generator to select a simple random sample of 500 students from a list of 70,000 student names. Describe how to implement such a method. (c) Because stratification can often provide a more precise estimate than a simple random sample, the third method the administrator is considering consists of selecting a stratified random sample of 500 students. The university has two campuses with male and female students at each campus. Under what circumstance(s) would stratification by campus provide a more precise estimate of the proportion of students who are satisfied with the appearance of the university buildings and grounds than stratification by gender? stratifying by campus would provide a more accurate astimate It the buildings & one campus greatly differ from the other campus (nower, mormodern, 0 better landscaping). 3. Each full carton of Grade A eggs consists of I randomly selected empty cardboard container and 12 randomly selected eggs. The weights of such full cartons are approximately normally distributed with a mean of 840 grams and a standard deviation of 7.9 grams. (a) What is the probability that a randomly selected full carton of Grade A eggs will weigh more than 850 grams? 850-840 -1.2658 P(2>1.2658)61028 7.9 (b) The weights of the empty cardboard containers have a mean of 20 grams and a standard deviation of 1.7 grams. It is reasonable to assume independence between the weights of the empty cardboard containers and the weights of the eggs. It is also reasonable to assume independence among the weights of the 12 eggs that are randomly selected for a full carton. Let the random variable X he the weight of a single randomly selected Grade A egg. i) What is the mean of X? ii) What is the standard deviation of X? 2 boxteggs = 2 2. boxesss 840-20-820 g eggs 68.23 g/egg 7.92 1.72+ 1252 59.52=1252 4.9652 S= 2.2271 g 4. The Behavioral Risk Factor Surveillance System is an ongoing health survey system that tracks health conditions and risk behaviors in the United States. In one of their studies, a random sample of 8,866 adults answered the question "Do you consume five or more servings of fruits and vegetables per day?" The data are summarized by response and by age-group in the frequency table below. Age-Group (years) No 18-34 231 741 972 35-54 669 2,242 2,911 55 or older 1,291 3,692 4,983 Total Yes 2,191 6,675 Total 8,866 Do the data provide convincing statistical evidence that there is an association between age-group and whether or not a person consumes five or more servings of fruits and vegetables per day for adults in the United States? Ho: There is no assoc b/w age-group d whether or Conormes 5t serving of fruits & veget/day net a person ha: There is an assoc b/w..... SRSV expected counts 35 YN 18-34 240.2 731.8 Expected cell counts. 35-54 71938 2191.6 55+ 1231.43751.6 @if = ((-1) (C-1)=2=2 2 X= 8.9834 p-valve ~ 0112 ww 8.9834 Reject the blk.0112 <.05. There is evidence to suggest that there is an assoc. blw age group & whether or not a person consumes 5t servings of fruits & vegetables in the us.