Practice Exam with Answer Key | Statistical Methods | STAT 303, Exams of Data Analysis & Statistical Methods

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Pract Exam – STAT-303-505-FALL-

ANSWERS ARE AT THE BOTTOM OF THE PAGE

Q9-11 is not part of Exam-1!!

In a statistics class with 136 students, the professor records how much money each student has in their possession during the first class of the semester. The histogram shown below represents the data he collected. Use this data for the next four questions. 0 10 20 30 40 50 60 70 80 90 100 110 Amount of money (in dollars) 0 10 20 30 40 50 60 70 Frequency 1.) What should we use to describe the center and spread for this distribution? A.) median and standard deviation B.) median and IQR C.) mean and standard deviation D.) mean and IQR E.) mean and range 2.) What term might we use to describe the student who has between 100 and 110 dollars? A.) third quartile B.) mode C.) categorical D.) outlier E.) intercept 3.) Which of the following is most likely true for this data set? A.) The median salary is greater than the average salary. B.) The average salary is greater than the median salary. C.) The average salary is approximately equal to the median salary. D.) The standard deviation is a good measure of spread for this data set. E.) The student who has between 100 and 110 dollars did not significantly affect the mean statistic.

Use the following to answer the next two questions: A researcher at a large company has collected data on the beginning salary and current salary of 48 randomly selected employees. The least-squares regression equation for predicting their current salary (measured 5 years from the employees’ hires) from their beginning salary is y ˆ^ = –2532.

• 2.12 x. 6.) Your friend Bob just got offered a job at this company making $25,000. What would you predict his salary will be in 5 years? A.) $55,532. B.) -$2,532. C.) $12,987. D.) $44,107. E.) $50,467. 7.) What is the meaning of the number 2.12 in the least-squares regression equation above? A.) If an employee got hired for volunteer work (for $0.00 per year), he will be making $2.12 after 5 years with the company. B.) The correlation between beginning salary and salaries 5 years later is 2.12. C.) Beginning salaries explain 2.12% of the variation in salaries five years later. D.) If Employee A is hired at $1.00 more than Employee B, then five years later, Employee A will be making $2.12 more per year than Employee B. E.) An employee hired at $1.00 per year is predicted to make $2.12 per year five years later. Answer the next two questions based on the following: A new reality show for gardeners called “Extreme Backyard Survivor” has just come out on HGTV. Contestants design landscapes for the backyard and plant them; then the backyards are exposed to severe wind and rains to simulate severe storms. Judges choose a winner based on both beauty in design and hardiness through the storm. Grandpa is an avid gardener and wants to become a contestant, so he is going to plant 12 of his favorite shrubs in his yard and find out which type of fertilizer works best and how much he should water his plants if he uses either of the fertilizers. To that end, he will fertilize the shrubs using 2 different fertilizers, water them with two initial watering levels (high and low), and measure the root depth (a good measure of whether the plants will survive the “storm”) after four weeks of growth. 8.) What is the response variable in this study? A.) watering level B.) type of shrub planted C.) beauty in design D.) root depth E.) fertilizer type

9.) What type of study is Grandpa conducting? A.) observational study B.) experiment, but not a double-blinded experiment C.) double-blinded experiment D.) confounding study E.) cluster experiment 10.) In order to select a sample of undergraduate students in the United States, a simple random sample of four states is selected. From each of these states, a simple random sample of two colleges or universities is then selected. Finally, from each of these eight colleges or universities, a simple random sample of 20 undergraduates is selected. The final sample consists of 160 undergraduates. What sampling technique is being used? A.) convenience sampling B.) stratified random sampling C.) cluster sampling D.) simple random sampling E.) multistage sampling 11.) In a recent study, doctors sampled records from several states and found that the average weight for 12-year-old children living in the US was 85 pounds, compared to the 12-year-old children living in France, who had an average weight of 82 pounds. Doctors’ records from across the country suggest that the true average weight of 12-year-old children living in the US is 86 pounds. Which of the following is true? A.) 86 is a parameter in this study, and 85 is a statistic B.) 82 is a parameter in this study, and 85 is a statistic. C.) 85 is a parameter in this study, and 86 is a statistic. D.) 12 is a parameter in this study, and 82 is a statistic. E.) 86 is a parameter in this study, and 12 is a statistic.

14.) Use the plot below to answer the following question.

A B C D E

ACT scores are normally distributed with a mean of 20.8 and a standard deviation of 4.8. SAT scores are normally distributed with a mean of 1000 and standard deviation of 200. Jeremy scored a 780 when he took the SAT. What point appears to lie closest to the ACT score that is equivalent to his SAT score? The length and width for a sample of products made by a certain company are plotted below. Use the information from the plot for the next two questions. 60.0 65.0 70.0 75.0 80. Width

Length The correlation between length and width (both measured in inches) is calculated to be r = 0.827. The equation for predicting length using width as the predictor variable is y ˆ^ = –112.75 + 4.17 x.

15.) Approximately what percent of variation in length of product is explained by width in this company? A.) 82.7% B.) 4.17% C.) 68.4% D.) 17.4% E.) 72.3% 16.) If we removed the point (79, 190.0), what would happen? A.) Since r is robust to outliers, it would not change. B.) R would decrease slightly. C.) R would increase slightly. D.) The slope of the line would become negative. E.) The intercept would increase noticeably. 17.) People who live in more northern states tend to have higher education levels than people living in southern states. Do US citizens’ IQs increase as one travels further north? We also find that people living in more northern states tend to have higher income levels. What kind of variable is income level? A.) categorical variable B.) lurking variable C.) response variable D.) A and B above E.) B and C above Use the following chart for the next three questions. This is from a study in which doctors were randomly placed into two groups: one to take aspirin every day, and the other to take a placebo. (Yes, the doctors were the patients in this study.) Neither the doctors taking the drugs nor the physicians examining them knew whether the doctor was taking the placebo or the aspirin. (A myocardial infarction is a dangerous episode having to do with the heart. Most of these are heart attacks. This data set comes from the New England Journal of Medicine, 1988.) 18.) What is the probability of having a myocardial infarction assuming that you are a doctor taking aspirin every day (rounded to 5 decimal places)? A.) 0.00914 (aka 9.14 × 10-03) B.) 0. C.) 0. D.) 0. E.) 0. Myocardial Infarction Group Yes No Total Placebo 190 10,840 11, Aspirin 100 10,930 11, Total 290 21,770 22,