MATH 1342Exam 1 – Page 2 of 113/1/2021 and 3/2/20212. (5 points) The following figure is a dotplot of a random sample of 200 ACT Math scores.Using the 95% Rule and counting dots, estimate the value of the standard deviation fromthe plot.
MATH 1342Exam 1 – Page 3 of 113/1/2021 and 3/2/20213. (13 points) From a random survey of US adults, 35 of 181 women had tried a low fatdiet while 8 of the 105 men had tried a low-fat diet.(a) (5 points) Create a two-way table of the data. Include row and column labels, aswell as totals across and down.(b) (2 points) What is the sample proportion of women who have tried a low-fat diet?(Use correct notation.)(c) (2 points) What is the sample proportion of men who have tried a low-fat diet?(Use correct notation.)(d) (2 points) Compute the difference in the sample proportions of men and womenwho have tried a low-fat diet?
MATH 1342Exam 1 – Page 4 of 113/1/2021 and 3/2/2021(e) (2 points) Which of the following is a correct interpretation of the difference in theproportions?A. In the sample, the proportion of those who have tried a low-fat diet whoare female is 0.117 more than the proportion of those who tried a low-fatdiet who are male.B. In the sample, the proportion of males and females who have tried alow-fat diet is 0.117C. In the sample, the proportion of males and females who have not tried alow-fat diet is 0.117D. In the sample, the proportion of females who have tried a low-fat diet is0.117 more than the proportion of males.E. In the sample, the proportion of males who have tried a low-fat diet is0.117 more than the proportion of females who have tried a low-fat diet.4. (14 points) An ad for Crest Whitestrips Premium claims that the strips will whitenteeth in 7 days and the results will last for 12 months. A researcher who wishes to testthis claim studies 20 pairs of adult identical twins. Within each pair of twins, one israndomly selected to use Crest Whitestrips Premium in addition to regular brushingand flossing, while the other just brushes and flosses. Whiteness of teeth is measured atthe beginning of the study, after 7 days, and every month thereafter for 12 months.(a) (2 points) What are the cases?(b) (2 points) What is the explanatory variable?(c) (2 points) What is the response variable?(d) (2 points) Is this an observational study, randomized comparative experiment or amatched pairs experiment?
MATH 1342Exam 1 – Page 5 of 113/1/2021 and 3/2/2021(e) (3 points) Say the Crest Whitestrips Premium group demonstrates a substantialimprovement in whiteness, can we infer that Crest Whitestrips Premium improveswhiteness of teeth? Why or why not?(f) (3 points) Can we generalize to the population of all adults? Why or why not?5. (5 points) I have a sample of 362 SAT scores from a particular college. A histogram ofthe data follows below. Each bin is 100 points wide. The first bin goes from 750 to 850,the second from 850 and 950, the third from 950 to 1050, and so on. Approximately,what percentage of the sample scored between 1050 and 1350?
MATH 1342Exam 1 – Page 6 of 113/1/2021 and 3/2/20216. (6 points) We ask a random sample of students enrolled in statistics at U.T., “What isthe typical amount of sleep you get per night?”(a) (2 points) Indicate the number of variables involved.(b) (2 points) Identify the variable(s) as being quantitative or categorical.(c) (1 point) Choose the appropriate type of graph that could be used to visualize datacorresponding to the question. (side-by-side boxplot,bar chart,histogram)(d) (1 point) Choose the appropriate statistic that could be used to summarize thedata corresponding to the question. (difference in proportions,single proportion,single mean,difference in means)7. (5 points) Are men or women more likely to support the death penalty?(a) (2 points) Indicate the number of variables involved.(b) (2 points) Identify the variable(s) as being quantitative or categorical.(c) (1 point) Choose the appropriate statistic that could be used to summarize the datacorresponding to the question (difference in proportions,single proportion,singlemean,difference in means)
MATH 1342Exam 1 – Page 7 of 113/1/2021 and 3/2/20218. (6 points) To answer the question, “Do men or women exercise more hours per week?”(a) (2 points) Indicate the number of variables involved?(b) (2 points) Identify the variable(s) as being categorical or quantitative.(c) (1 point) Choose the appropriate type of graph that could be used to visualize datacorresponding to the question. (side-by-side boxplot,bar chart,histogram)(d) (1 point) Choose the appropriate statistic that could be used to summarize thedata corresponding to the question. (difference in proportions,single proportion,single mean,difference in means)9. (6 points) A random sample of 1500 high school students was asked, “Have you usedmarijuana in the last three months?”(a) (2 points) Indicate the number of variables in the study.(b) (2 points) Classify the variable(s) as categorical or quantitative.(c) (1 point) Choose the appropriate type of graph that could be used to visualize thedata. (side-by-side boxplot,bar chart,histogram)(d) (1 point) Choose the appropriate statistic that could be used to summarize thedata. (single proportion,difference in proportions,single mean,difference in means)
MATH 1342Exam 1 – Page 8 of 113/1/2021 and 3/2/202110. (11 points) Morelia, a recent high school student, took the ACT exam in 2014 and gota score of 34 on all three components (English, Math, Reading). In other words, herEnglish score was 34, her Math score was 34, and her Reading score was 34. She wasinterested in how well she did relative to her peers. The following table shows thesummary statistics for all students in 2014.Component Mean Standard DeviationEnglish20.27.0Math20.55.5Reading21.36.8(a) (5 points) Calculate thez-scores for all three of Morelia’s scores.(b) (2 points) Which of Morelia’s three scores is the most extreme relative to her peers?(c) (2 points) Which of Morelia’s three scores is the least extreme?(d) (2 points) On which of the three tests did Morelia do best relative to her peers?
MATH 1342Exam 1 – Page 9 of 113/1/2021 and 3/2/202111. (12 points) A statistician frequents Archie’s Seabreeze Bar and Grill and is interested in amount wings eaten by female and male patrons at this establishment. Data collected from samples of 15 females and 15 males and summary statistics follow.Females4556778911 12 12 13 13 14 14Males788 11 13 13 14 1616 17 17 18 18 21 21Descriptive Statistics: wings Variable gender N Mean StDev Minimum Q1 Median Q3 Maximum wings F 15 9.333 3.559 4.000 6.000 9.000 13.000 14.000M 15 14.53 4.50 7.00 11.00 16.00 18.00 21.00(a) (2 points) Indicate the mean number of wings eaten by the females in the sample using correct notation.(b) (2 points) Indicate the mean number of wings eaten by the males in the sample using correct notation.(c) (2 points) Compute the difference between the sample mean number of wings formales and the sample mean number of wings for females. (Use correct notation.)
MATH 1342Exam 1 – Page 10 of 113/1/2021 and 3/2/2021(d) (2 points) Choose the correct interpretation of the difference between the two means.A. In the sample, the mean number of wings for males is 5.197.B. In the sample, the mean number of wings for males is 5.197 less than theme an number of wings for females.C. In the sample, the mean number of wings is 5.197.D. In the sample, the mean number of wings for males is 5.197 more than the mean number of wings for females.E. In the sample, the mean number of wings for females is 5.197.(e) (4 points) Consider the side-by-side boxplot for the data that follows. The circles inside the boxes represent means. Does the plot suggest a relationship between gender and the number of wings eaten? Explain your answer.
MATH 1342Exam 1 – Page 11 of 113/1/2021 and 3/2/202112. (7 points) We have some data from a particular state regarding drownings and incidence of Lyme Disease, a disease carried by ticks. The cases are the 12 months of the year, and the variables are number of drownings and the number of cases of Lyme Disease. The data show a very strong association between the two. The nature of the association is hat as the number of Lyme Disease cases increases the number of drownings increases.Which of the following could be an explanation of the confounding? Choose all that apply, and identify the confounding variable in each of the ones you select
.A The fact that less and less people are learning how to swim explains why so many people are drowning.The confounding variable is(only if selected)
.B Lyme Disease is on the rise because products previously used to repel ticks have been determined to be harmful to the environment.The confounding variable is (only if selected).
C When it is warmer out, more people are outdoors getting bitten by ticks and thus getting Lyme Disease, and more people are in the water leading to more drownings.The confounding variable is (only if selected)
D People are going to drown regardless of whether they or others are getting Lyme Disease.The confounding variable is (only if selected).