STAB22 Midterm Review Seminar June 18, 2019 STAB22 2014 Midterm Test Presented by Sohee Kang

1. The histogram of the annual family income (in dollars) of a random sample of 200 families selected from a population is shown below. Without actually finding the mean and the median, would you expect the mean to be higher or lower than the median and why? (a) Mean should be lower than the median, because the distribution of this data is skewed to the left. (b) Mean should be higher than the median, because the distribution of this data is skewed to the right. (c) Mean should be higher than the median, because the distribution of this data is skewed to the left. (d) Mean should be lower than the median, because the distribution of this data is skewed to the right. (e) Mean should be equal to the median, because the distribution of this data is skewed to the right.

2. A new tax law is expected to benefit “middle income" families, those with annual family income between $20 000 and $30 000. If the annual family income in this population has a Normal distribution with mean $25 000 and standard deviation $10 000, what percentage of the families in this population will benefit from the law? (a) 10 percent (b) 19 percent (c) 38 percent (d) 50 percent (e) 76 percent 3. The reaction time of 20 drivers at a stop light was measured, in seconds, as the time between the traffic light turning green and the time it took them to press the gas pedal. These values are given below: 0.4, 1.0, 1.5, 1.6, 2.2, 2.2, 2.4, 2.7, 3.4, 3.4, 3.5, 3.6, 3.6, 3.7, 3.7, 3.7, 4.1, 4.2, 4.2, 7.0 Use 1.5 x IQR rule to identify outliers. (a) 0.4 and 7.0 are outliers. (b) 4.2 and 7.0 are outliers. (c) Only 0.4 is an outlier. (d) Only 7.0 is an outlier. (e) Based on 1.5 IQR rule, there are no outliers in this data set.

4. In a small survey a researcher recorded the lengths (in seconds) of 24 telephone calls. The boxplot below represents the lengths of these 24 calls: Consider the following statements regarding the distribution of the length of these calls, each of which is either true or false. I The distribution of the length of these calls is skewed to the left. II The third quartile of the lengths of these calls is 600 seconds. III The interquartile range of the length of these calls is greater than 300 seconds. Which of these statements is (are) true? (a) Only statement I is true (b) Only statement II is true (c) Only statement III is true (d) All three statements are true (e) None of the statements is true 5. The five-number summary for the exam scores in a statistics class is 30, 67, 77, 83, 96. This class had 196 students. How many students had scores between 77 and 83? (In order to avoid unnecessary complications, assume that none of the students in this class scored exactly 77 or 83.) (a) 6 (b) 39 (c) 49 (d) 98 (e) It cannot be determined from the information given.

6. The grades in an exam has a Normal distribution with mean 65 6. The grades in an exam has a Normal distribution with mean 65. The density curve of this Normal distribution and the area under the curve between 49 and 81 is below: What is the standard deviation of this Normal distribution? (a) 65 (b) 2 (c) 4 (d) 8 (e) 16 7. The IQ scores of a large group of students has Normal distribution with mean 100 and standard deviation 15. What proportion of students in this group have an IQ score greater 110? (a) 12.5 percent (b) 25 percent (c) 30 percent (d) 50 percent (e) 75 percent

8. Scores for a civil service exam are normally distributed with a mean of 75 and a standard deviation of 6.5. To be eligible for civil service employment, you must score in the top 5%. What is the lowest score you can earn and still be eligible for employment? (a) 83 (b) 86 (c) 88 (d) 90 (e) 95 9. A consumer reporting magazine published an article evaluating infant car seats in Canada. It listed 10 models, giving the brand, cost, age limit, weight limit, and overall safety rating. Which of the following choices correctly identifies the W's (This question is only interested in three W's: Who the individuals are, What the variables are and Why did they collect that information. Please identify the choice that identifies all these three W's correctly.) (a) Who: 10 infant car seat models; What: Overall safety rating; Why: To provide information to readers (b) Who: Magazines; What: Articles; Why: To provide information to readers (c) Who: Consumer reporting magazine; What: Infant car seat models; Why: To provide information to readers (d) Who: 10 infant car seat models; What: Brand, cost, age limit, weight limit, and overall safety rating; Why: To provide information to readers (e) Who: Consumers; What: Brand, cost, age limit, weight limit, and overall safety rating; Why: To educate infants

10. The bar chart below shows the distribution of grades in a Statistics class. What percentage of the students in this class got A's? (a) 10 percent (b) 20 percent (c) 25 percent (d) 30 percent (e) 35 percent 11. The stemplot of the annual salaries of 19 employees in a company is given below: Variable: Salary Decimal point is 3 digit(s) to the right of the colon. 34 : 8 35 : 02 36 : 0 37 : 135679 38 : 07 39 : 226 40 : 07 41 : 03 What is the median annual salary of these employees? (a) $ 37 000 (b) $ 37 500 (c) $ 37 900 (d) $ 38 000 (e) $ 379 000

12. The stemplot of the weights (in Kg) of 22 babies is given below: Variable: weight Decimal point is at the colon. 2 : 78 3 : 0233334 3 : 567788 4 : 111244 4 : 5 What is the interquartile range (IQR) of these weights? (a) 3.1 kg (b) 0.4 kg (c) 8.0 kg (d) 0.8 kg (e) 4.0 kg 13. The histogram shows the distribution of the sizes (in acres) of 169 farms in Ontario. Assume that there were no farms with size exactly equal to any of the class boundaries of this histogram. Consider the following statements regarding the distribution of the sizes of farms in Ontario, each of which is either true or false. I The distribution of the sizes of farms is skewed to the left. II More than 65 percent of the farms in Ontario are smaller than 100 acres in size. III There is only one farm larger than 400 acres in size. Which of these statements is (are) true? (a) Only statement I is true (b) Only statement II is true (c) Only statement III is true (d) All three statements are true (e) None of the statements is true