Sample Exam 1 Math 263 (sect 9) Prof. Kennedy

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1 Sample Exam 1 Math 263 (sect 9) Prof. Kennedy 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 she collected: (a) What is approximately the percentage of students with under $10.00 in their possession? A) 35% C) 44% B) 40% D) 50% (b) The median is approximately A) 2$ C) 20$ B) 11$ D) 55$ (c) The median will be (i) to the right of the mean (ii) to the left of the mean (iii) equal to the mean (iv) can t say (d) The IQR is approximately A) 10$ C) 30$ B) 15$ D) 110$ (e) The bar between 10$ and 20$ has a height of 42. Write one sentence explaining what this tells us about the students.

2 2. A market research company employs a large number of typists to enter data into a computer database. The time it takes for potential new typists to learn the computer system is known to have a Normal distribution with a mean of 90 minutes and a standard deviation of 18 minutes. A candidate is automatically hired if she learns the computer system in less than 100 minutes. A cut-off time is set at the slowest 10% of the learning distribution. Anyone slower than this cut-off time is definitely not hired. (a) (b) (c) What proportion of candidates takes more than two hours to learn the computer system? What proportion of candidates will be hired automatically? What is the cut-off time the market research company uses? (d) Suppose we know the distribution is normal with a mean of 90, but we do not know the standard deviation. We do know that 75% of the times are between 75 and 105 mins. What is the standard deviation? 3. The weights of packets of cookies produced by a certain manufacturer have a Normal distribution with a mean of 202 g and a standard deviation of 3 g. What is the weight that should be stamped on the packet so that only 1% of packets are underweight? 4. A sample was taken of 20 salaries of employees in a large company. The following are the annual salaries (in thousands of dollars). For convenience, the data have been ordered (a) (b) (c) What is the median salary of the 20 employees? What is the first quartile of the 20 salaries? What is the interquartile range of the 20 salaries? (d) Suppose each employee in the company receives a $3000 raise for next year (each employee s salary is increased by $3000). For each of the following summary measures, indicate how it would change after the raise. A) The median salary. B) The interquartile range of the salaries. C) The standard deviation of the salaries. A boxplot of a different sample of 20 salaries from this same company is shown below:

3 (e) For each of the following sentences, fill in the blank. A) The maximum salary is approximately dollars. B) The minimum salary is approximately dollars. C) The interquartile range is approximately dollars. D) Seventy-five percent of the employees in this sample of 20 earn more than approximately dollars. (f) Based on this boxplot, answer each of the following questions with yes, no, or can t tell. A) Is the salary distribution heavily skewed? B) Do about 10 employees make more than $55,000? C) Does nobody make more than $71,000? D) Is the range of the salaries roughly $35,000?

4 5. Match the four graphs labeled A, B, C, and D, with the following four possible values of the correlation coefficient: 0.9, 0.7, 0.4, Assume all four graphs are made on the same scale. A) B) C) D)

5 6. Eight students take the SAT test and then two months later take the ACT. The results are: Student SAT ACT Treat the SAT score as the explanatory variable and the ACT score as the response variable. (a) Find the correlation coefficient r. (b) Find the equation of the regression line. (c) Is it reasonable to conclude from this data that there is a casual relationship between the two test? Explain your answer. (d) Use your regression line to predict the ACT score of a student who gets 1225 on the SAT. (e) Give a one sentence explanation of what the slope in your regression line equation means.

STAT 2300: Unit 1 Learning Objectives Spring 2019

STAT 2300: Unit 1 Learning Objectives Spring 2019 Unit tests are written to evaluate student comprehension, acquisition, and synthesis of these skills. The problems listed as Assigned MyStatLab Problems