STS XM

A law firm has 30 attorneys, 15 of whom are associates and 15 of whom are partners. Each associate is paired with a partner as a mentor. The following lists are available: a list of the 15 pairs; a list of the 15 associates; a list of 15 partners; and a list of the 30 attorneys. For each question, identify the sampling plan used to select the sample of attorneys. (a) Twelve attorneys are randomly selected from the list of the 30 attorneys. (b) The sample of n = 5 consists of the first five attorneys who arrived for work at the firm on Thursday of last week.

(a) E. Simple random sample. (b) A. Convenience or haphazard sample.

A trucking fleet-owner owns two semi-trucks and wishes to compare the amount of fuel used per week by the two vehicles. In a random sample of 100100 weeks, truck #1 used a mean volume of 400400 gallons with a standard deviation of 1111 gallons. In a second, independent random sample of 100100 weeks, truck #2 used a mean volume of 386386 gallons with standard deviation 77 gallons.It is of interest to construct a confidence interval for the difference in population means using a confidence level of 90 percent. 𝜇1−𝜇2μ1−μ2, where 𝜇1μ1 is the mean fuel volume used by truck #1 and 𝜇2μ2 is the mean volume of fuel used by truck #2. Note: 400−386=14400−386=14 and 112100+72100‾‾‾‾‾‾‾‾‾‾‾√=1.30384048104053112100+72100=1.30384048104053 Your answers below should be entered as numbers. Do not round during intermediate steps. If you round an answer, make sure you do so correctly and keep at least three decimal places.

(a) The estimate is: 14 gal (b) The standard error is: 1.30384 (c) The multiplier is: 1.645

(a) A population of measurements is approximately normal with a mean of 95 and a standard deviation of 15. The percentage of measurements that are 124.4 or HIGHER is (b) A population of measurements is approximately normal with a mean of 110 and a standard deviation of 20. A particular measurement was 135.6. What is the PERCENTILE rank of this measurement?

(a)C. 2.5% (b)B. 90th percentile

(20 points) Two separate random samples of workers from a particular industry were selected with the following results. (a) If sample 1 is used to estimate the population percentage, what is the margin of error? Enter the margin of error as a percentage rounded to one decimal place: (b) If sample 2 is used to estimate the population percentage, then an interval that (in the terminology of our formula packet) "almost certainly" contains the true population percentage is:

9.44911 37 ; ask shay

(a) Find the p - value for the test statistic 𝑧=1.75z=1.75 for the following null and alternative hypotheses:𝐻0:𝜇=50H0:μ=50𝐻𝐴:𝜇>50HA:μ>50The p - value is (0.04) (b) Find the p - value for the test statistic 𝑧=1.88z=1.88 for the following null and alternative hypotheses:𝐻0:𝜇=50H0:μ=50𝐻𝐴:𝜇≠50HA:μ≠50The p - value is (0.06)

= 0.04 = 0.06

A random sample 4949 restaurant patrons were found to have a mean age of 𝑥⎯⎯⎯=30x¯=30 with standard deviation of 𝑠=12.s=12. Find the value of the test statistic 𝑧z for evaluating the null hypothesis 𝜇=35.μ=35. NOTES: ∙∙ Your answer below should be entered as a number. Do not round during intermediate steps. If you round your answer, make sure you do so correctly and keep at least three decimal places. ∙∙ The answer you enter should be the z-score you computed. (You should NOT enter the closest z value that is an entry in our normal table.) The test statistic is 𝑧z = ()

-2.91667

The t statistic for a test of 𝐻0:𝜇=8H0:μ=8 𝐻𝐴:𝜇>8HA:μ>8 based on n = 17 observations has the value t = 1.72. Using the appropriate table in your formula packet, bound the p-value as closely as possible. In the blank below, you should enter the LOWER BOUND on the p-value (the upper bound is given). < p-value < 0.059

0.045

The t statistic for a test of 𝐻0:𝜇=33H0:μ=33 𝐻𝐴:𝜇≠33HA:μ≠33 based on n = 21 observations has the value t = 1.85. Note that the alternative hypothesis has ≠≠ in it, which will affect the process by which you bound the p-value below. Using the appropriate table in your formula packet, bound the p-value as closely as possible. In the blank below, you should enter the UPPER BOUND on the p-value (the lower bound is given). 0.06 < p-value <

0.086

The t statistic for a test of 𝐻0:𝜇=15H0:μ=15 𝐻𝐴:𝜇<15HA:μ<15 based on n = 10 observations has the value t = -1.32. Using the appropriate table in your formula packet, bound the p-value as closely as possible. In the blank below, you should enter the UPPER BOUND on the p-value (the lower bound is given). 0.084 < p-value <

0.116

20 points) The t statistic for a test of 𝐻0:𝜇=59H0:μ=59 𝐻𝐴:𝜇≠59HA:μ≠59 based on n = 6 observations has the value t = -1.61. Note that the alternative hypothesis has ≠≠ in it, which will affect the process by which you bound the p-value below. Using the appropriate table in your formula packet, bound the p-value as closely as possible. In the blank, you should enter the LOWER BOUND on the p-value (the upper bound is given). < p-value < 0.194

0.16

(17 points) Weights of a certain breed of dog approximately follow a bell-shaped (normal) frequency curve with mean = 80 pounds and standard deviation = 4 pounds. (a)According to the empirical rule, the approximate percentage of dogs that weigh between lower-bound = 76 pounds and upper-bound = 84 pounds is (68%) (b) According to the empirical rule, approximately 99.7 percent of dogs weight between lower-bound = (68%) = pounds and upper-bound == 92 pounds

68 - 95 - 99.7 (a) see # between low and high (b) find low; low = (a) answer/68 high=92

Consider testing 𝐻0:𝑝=.50H0:p=.50𝐻𝑎:𝑝<.50Ha:p<.50 Note: Make sure you answer this question using the normal table on page #5 of your formula packet. Do NOT use a calculator or other means of determining normal curve areas. If the sample information produced a test statistic of 𝑧=−0.84z=−0.84, then p-value =

= 0.2

(13 points) A sample of 40 adult Randolph County residents showed that 24 own a home. What is the RISK of owning a home? (If you round your answer, make sure you do so correctly keeping at least three decimal places.)

= 0.6

(6 points) A particular variable measured on the US population is approximately normally distributed with a mean of 124 and a standard deviation of 20. Consider the sampling distribution of the sample mean for samples of size 4. Note that 20/√4=10

= 154

(14 points) Two separate samples, each of one-thousand residents over the age of 25, were selected for two counties in Missouri. For each county, the risk of being a college graduate is shown below. Boone County: Risk = 0.508 Cooper County: Risk = 0.23 If you round your answer, make sure you do so correctly keeping at least three decimal places. For the populations considered, the RELATIVE RISK of being a college graduate for Boone County as compared to Cooper County is (2.2087)

= 2.2087

A measurement is normally distributed with 𝜇=67μ=67 and 𝜎=20σ=20. Note that 20/√4=2.5 (a) The mean of the sampling distribution of 𝑥¯x¯ for samples of size 𝑛=64n=64 is: (b) The standard deviation of the sampling distribution of 𝑥¯x¯ for samples of size 𝑛=64n=64 is:

= 67 = 2.5

(a) The fact that a survey concerning the cost of college education was conducted immediately following a tuition increase at the local state university. (b) The fact that a study was originally published in The Journal of the American Statistical Association.

A. Component 5: Setting. A. Component 1: Source.

(a) In a hypothesis testing context, before examining the data, one should (b) In general, there is more information provided by

A. decided whether the alternative hypothesis is one-sided or two-sided. C. a confidence interval than a p-value.

(13 points) An airlines utilizes two different types of planes (A and B) and serves four destination sizes (very large cities, large cities, mid-sized cities, and small cities). A sample of 677 passengers were classified according to the type of plane on which they flew and the size of market to which they were travelling. The results are shown below. The chi-squared value is 𝜒2=χ2= 23.04 Using 𝛼=0.05α=0.05, consider a test of 𝐻0:H0: type of plane and size of destination are not related vs. 𝐻𝐴:HA: type of plane and size of destination are related. Note that this problem involves a 4×24×2 contingency table and that the magic number for evaluating such a table at the 𝛼=0.05α=0.05 level of significance is magic number = 7.81.

A. reject H0, There is sufficient evidence to conclude that type of plane and size of destination are related.

(a) An experiment involved the response variable resting pulse rate and the explanatory variable diet (low-sodium; standard). For subjects under the age of thirty, it was found that resting pulse rates were the same for the two groups. However, for subjects age thirty or older, the study showed that resting pulse rates were lower for subjects on the low-sodium diet. This information suggests that age (under 30 years; 30 years or older) (b) A study was conducted in order to compare the ages of two groups: Mizzou sophomores and UMSL sophomores. The Explanatory variable is

B. interacts with diet (low-sodium; standard). B. GROUP (Mizzou sophomores or UMSL sophomores).

(a) The proportion of z-scores from a normal distribution that are LARGER than z = 0.10 is (b) The proportion of z-scores from a normal distribution that are LARGER than z = -1.00 is

D. 0.46 C. 0.84

(a) Consider the following variables measured on undergraduate students who attend the University of Missouri. Which of these variables is categorical? (b) Consider the following variables measured on undergraduate students who attend the University of Missouri. Which of these variables is categorical?

D. The name of the last high school the student attended. C. The student's favorite color.

Two online retailers offer a particular style of webcam for sale. The prices of these cameras vary day by day. Consider two groups: Group #1 consists of consumers who purchased a camera from retailer #1 during the past three months and Group #2 consistes of consumers who purchased a camera from retailer #2 during the same period of time. A 99% confidence interval for 𝜇1−𝜇2μ1−μ2, the difference in population mean sale prices, is 30 to 60 dollars. (b) The confidence interval provides no strong evidence to support or refute the claim that, on average, students who purchased a camera from retailer #1 spent __________ dollars more than those who purchased a camera from retailer #2.

D. more than 50 B. at least 25

(a) The variables considered in a chi-squared test used to evaluate a contingency table (b) a x^2 statistic provides strong evidence in favor of the alternative hypothesis if its value is

E. are categorical. E. a large positive number.

For each statement, select the correct null hypothesis, 𝐻0H0, and alternative hypothesis, 𝐻𝐴HA, in symbolic form. (a) It is generally believed that the population mean age of residents of Cooper County is 40 years. A sociologist believes that, in reality, the population mean is less than generally believed. In order to collect evidence, the sociologist randomly samples 100 Cooper County residents and found the sample mean age to be 38.5 years.

F. 𝐻0:𝜇=40H0:μ=40 , 𝐻𝐴:𝜇<40 A. 𝐻0:𝜇=50H0:μ=50, 𝐻𝐴:𝜇≠50 C. 𝐻0:𝜇=45H0:μ=45, 𝐻𝐴:𝜇>45

(16 points) A nationwide award for high school students is given to outstanding students who are sophomores, juniors, or seniors (freshmen are not eligible). Of the award-winners, 65 percent are SENIORS, 20 percent JUNIORS, and 15 percent are SOPHOMORES. (a) Suppose we select award-winners one at a time and continue selecting until a SENIOR is selected. What is the probability that we will select exactly 3 award-winners? (b) Suppose we select award-winners one at a time and continue selecting until a JUNIOR is selected. What is the probability that we will select more than 2 award-winners? (c) Suppose we select award-winners one at a time continue selecting until a SOPHOMORE is selected. What is the probability that we will select 2 or fewer award-winners?

a = 0.079625 b = 0.64 c = 0.2775

(16 points) A random sample of 80 University of Missouri sophomores showed that 28 were planning to live off-campus next semester. Suppose that we are interested in forming a 99.7 percent confidence interval for the proportion of all Mizzou sophomores who are planning to live off-campus next semester. Note that 2880=0.352880=0.35 and (0.35)(1−0.35)80‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√=0.0533268225192539 NOTE: Where appropriate, express your answer as a proportion (not a percentage). Do not round during intermediate steps. If you round an answer, make sure you do so correctly and keep at least three decimal places.

a = 0.35 b = 0.0533268 c = 3

(16 points) Of recent college graduates, 0.76 proportion moved, 0.42 proportion bought a car, and 0.28 proportion moved and bought a car. NOTE: Your answers below should be entered as decimal numbers. Do not round during intermediate steps. If you round an answer, make sure you do so correctly and keep at least three decimal places. (a) One graduate will be selected at random. What is the probability that the selected graduate will have moved or bought a car (or both)? (b) One graduate will be selected at random. What is the probability that the selected graduate will NOT have moved? (c) Two graduates will be independently selected at random. What is the probability that both of the selected graduates will have bought a car?

a = 0.9 b = 0.24 c = 0.1764

(16 points) For a particular large group of people, blood types are distributed as shown below. (Note that each person is classified as having exactly one of these blood type (meaning that, for a particular person, blood types are mutually exclusive).) (a) If one person is selected at random, what is the probability that the selected person's blood type will be either AB or O? (b) If two people are independently selected at random, what is the probability that both will have type O blood? (c) A person who has type B blood can safely receive blood transfusions from people whose blood type is either O or B. If a person is selected at random, what is the probability that the selected person will be able to safely donate blood to a person with type B blood?

a = C. 0.46 b = C. 0.0529 c = B. 0.35

(20 points) At a certain high school, for seniors, the odds in favor of planning to attend college are 3.9 to 1. Of juniors at the same high school, 0.75 proportion plan to attend college. (a) For seniors, the PROPORTION who plan to attend college is (0.795918) (b) For juniors, the ODDS in favor of planning to attend college are (3) to 1.

solve

In a particular county, the population proportion of residents were born in the county is 0.7. Consider the sampling distribution of 𝑝̂ p^ = the sample proportion of residents in a sample of 𝑛=200n=200 who were born in the county. Note that (0.7)(1−0.7)200‾‾‾‾‾‾‾‾‾‾‾‾‾√=0.0324037034920393(0.7)(1−0.7)200=0.0324037034920393 NOTE: Your answers below should be entered as proportions (not percentages). Do not round during intermediate steps. If you round an answer, make sure you do so correctly and keep at least three decimal places. (a) The mean of the sampling distribution of 𝑝̂ p^ is: (0.7) (b) The standard deviation of the sampling distribution of 𝑝̂ p^ is: (0.0324037)

solve = 0.7 = 0.0324037

A game of chance involves rolling a special 10-sided die whose sides are numbered 1 through 10. (Note that this die has TEN sides.) The amount of money the player wins depends on the result of the die roll: * If the result is 1, 2, 3, or 4, the player wins nothing; * If the result is 5, 6, 7, 8, or 9, the player wins 24 dollars; * If the result is 10, the player wins 470 dollars. NOTE: Your answer below should be entered as a number. Do not round during intermediate steps. If you round your answer, make sure you do so correctly and keep at least three decimal places. If you play this game once (and it costs you nothing to play), what is the EXPECTED VALUE of the amount of money you will win?

solve = 59 dollar

For a sample of five students, the amount of time in hours each studied for an exam (x) and the score on the exam (y) were recorded. In the sample, the least amount of time studied was one hour and the greatest amount of timed studied was six hours. The equation of the least squares line is 𝑦=66+4𝑥. If a student studied 2.25 hours for the exam, what score does the least square line predict the student achieved? (If you round your answer, make sure you do so correctly keeping at least three decimal places.)

solve 𝑦=66+4𝑥. = 75

(13 points) For a sample of five married couples, the variables x = age of younger partner and y = age of older partner were recorded. The data show that SSX = 126.8, SXY = 124, SSY = 166, 𝑥¯x¯ = 27.2, and 𝑦¯y¯ = 31. Compute the slope of the least squares line. If you round your answer, make sure you do so correctly keeping at least three decimal places.

use formula; = 0.977918