Understanding Variables and Statistics in Graduate Outcomes and Health

1. Gallup conducted research to measure recent college graduates’ career and life outcomes. A 2014 study collected information about graduates’ annual income, whether they were living with their parents, employment status (employed or unemployed), zip code, their undergraduate grade point average (GPA), and whether the graduate was a member of a sorority/fraternity in college. a. What are the quantitative variables? Circle correct answer(s). There may be more than one correct answer. Annual income Living with Parents? Employment Status Zip code Undergraduate GPA Sorority/fraternity member b. What are the categorical variables? Circle correct answer(s). There may be more than one correct answer. Annual income Living with Parents? Employment Status Zip code Undergraduate GPA Sorority/fraternity member

2. A histogram, boxplot, and summary statistics are given for levels of calcium concentration in drinking water for 172 locations. Summary statistics: Calcium (ppm) n Median Range Min Max Qi Qs 172 102.6 478.8 34.2 513 68.4 205.2 Frequency 52 401 3071 28 ’ 25 23 ’_’23 | I L 2071 I 101 E 4 3 3 B2 0 100 200 300 400 500 100 200 300 400 500 Calcium (ppm) Calcium (ppm) a) Use the histogram to answer this question. What percent of locations had calcium concentrations of 250 ppm and above? Round your decimal to 3 decimal places, then report the corresponding percent (e.q., you would round .1248 to . 125 and then write 12.5%). I b) Use the summary statistics to determine the value of the upper fence (the upper fence is the upper limit using the 1.5*(IQR) criteria). Round your answer to the nearest whole number. Upper fence: ¢) Which of the following statements about the mean and median for this data is true? Circle the ONLY ONE correct statement. i) The mean calcium (ppm) is greater than the median calcium (ppm) because the distribution is skewed left. ii) The mean calcium (ppm) is greater than the median calcium (ppm) because the distribution is skewed right. iii) The median calcium (ppm) is greater than the mean calcium (ppm) because the distribution is skewed left. iv) The median calcium (ppm) is greater than the mean calcium (ppm) because the distribution is skewed right.

A survey was conducted to see how many phone calls people made daily. The results are displayed in the table below: Number of calls made Frequency 1-4 16 5-8 11 9-12 5 13-16 3 Y 17 — 20 2 1. How many of the people surveyed make more than 8 phone calls daily? ) 3 ) 8 ) 10 (5 + 3+ 2) ) 21 ) o O T O 27 L) 5. How many people were surveyed? 7.2 20 37 (16 + 11 +5+3+2) 226 O T o S e o N 6. Within which interval will the median fall? a) 1-4 b) 5 -8 (The median value will be the 19" value when ordered from smallest to largest. The 19" value is in the interval 5 -8) c) 9-12 d) 13-16 e) 17-20

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Scenario: Depression In the workplace, depression is a leading cause of absenteeism and loss of productivity (Greenberg, et al. 1993). To assess the degree to which people suffer from depression, prior to receiving treatment, data were collected on the number of days that 105 patients were depressed prior to starting a new treatment. These data are displayed in the following histogram: Histogram of Depression Days Frequency - (4] 40 80 120 160 200 240 280 320 360 400 440 480 520 Depression Days 1. What is wrong with this graph? a. Tick marks should be at the cutpoints (endpoints of intervals) not at the midpoint. b. Title is not descriptive enough. c. The labels are not descriptive enough. 2. Which of the following is a possible value of the median number of days that patients were depressed? a) 53 b) 170 (The median is the 53 value which must lie between 140 and 180.) c) 220 d) 290 3. Using this same histogram of 105 patients, which of the following is most likely to be true? a) The mean will be larger than the median (Since the distribution is skewed to the right, the mean will most likely be larger than the median.) b) The median will be larger than the mean c) The mean and median will be about the same

Histogram of Depression Days Frequency [==1 ()] 40 80 120 160 200 240 280 320 360 400 440 480 520 Depression Days 4. Using this same histogram of 105 patients, what percentage of patients had 220 or more days of depression? 10% 13% 18% 23% O T o ~— ~— o N 4. Using this same histogram of 105 patients, which of the following statements must be true a) More than half of the patients had fewer than 160 days of depression b) More than half of all patients had between 140 and 260 days of depression ¢) 20 patients reported having exactly 120 days of depression d) The mean number of days of depression is between 140 and 180 days

Scenario: Americans Without Health Insurance The United States federal government collects information on Americans who do not have health insurance. Data from 2004 are broken down into 4 regions of the country. These data are summarized in the table provided below. Using this table, answer the following questions. Region Uninsured Insured Total Northeast 6,782 47,043 53,825 Midwest 7,757 57,135 64,832 South 19,030 85,800 104,830 West 11,676 55427 67,103 Total 45,305 245 405 230,710 from 2004 census data figures in thousands of people 1) Based on these figures, what percent of the Midwestern Americans who were surveyed are uninsured? Round your decimal to 3 decimal places, then report the corresponding percent (e.g., you would round .1248 to .125 and then write 12.5% 2) Based on these figures, what percent of all the Americans surveyed are from the West? Round your decimal to 3 decimal places, then report the corresponding percent (e.g., you would round 1248 to .125 and then write 12.5%. 3) Based on these figures, what percent of all Americans surveyed are from the South and are uninsured? Round your decimal to 3 decimal places, then report the corresponding percent (e.g., you would round .1248 to .125 and then write 12.5%.

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30% of female statistics students have tattoos. Suppose we take a random sample of 4 female statistics students. Let X represent the number of students with tattoos. This situation can be modeled with a binomial random variable X. The probability distribution function and the cumulative distribution function for X is shown below. X P(X=x) 0 0.2401 1 0.6517 2 0.9163 3 0.9919 4 1.0000 1. What is the probability that exactly 2 students have tattoos? 2. What is the probability that at least 3 students have tattoos? (HINT: see the formula sheet for help using Cumulative Probability Distributions) 3. What is the probability at most 2 students have tattoos? 4. Determine the mean and standard deviation of X. Round all answers to 3 decimal places.

As of October 2015, 22% of American families had their credit card information stolen by hackers. Suppose we take a random sample of 8 American families. This situation can be modeled with a binomial random variable X. The cumulative distribution function (CDF) for X is shown below. P(XSx) oo NOoO O,k WODN ~O 0.13701 0.44617 0.75136 0.92351 0.98421 0.99791 0.99984 0.99999 1.00000 What is the probability that exactly 3 families out of the random sample of 8 families had their credit card information stolen by hackers? (HINT: see the formula sheet for help using Cumulative Probability Distributions) What is the probability that at least 3 families out of the random sample of 8 families had their credit card information stolen by hackers? (HINT: see the formula sheet for help using Cumulative Probability Distributions) Determine the mean and standard deviation of X. Round all answers to 3 decimal places.

Based on data from the Centers for Disease Control and Prevention on births in the United States in recent years, out of 3,952,841 births: e 456,553 births are preterm (under 37 weeks) e 130,839 births are to twins e 4919 births are to triplets and higher order multiple births. 1. Based on the available data, what is the estimated probability of a pre-term birth? Show all work. 2. Based on the available data, what is the estimated probability of a multiple birth (i.e., more than one child)? Show all work. 3. Based on the available data, what is the estimated probability that a multiple birth is to triplets and higher order? Show all work.

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2 STAT100_Test1_Practice_Problems

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