Name: PID: A STT 315 Section 101 05/19/2014 Quiz 1A 50 minutes 1. A survey by an electric company contains questions on the following: Age of household head, Gender of household head and use of electric heating (yes or no). For each of those variables circle the correct choice for its type. (3 pts total, 1 pt each) (i) Age of household head (ii) Gender of household head (iii) Use of electric heating Quantitative / Qualitative Quantitative / Qualitative Quantitative / Qualitative 2. The total points scored by a basketball team for each game during its last season have been summarized in the table below. Which of the statements following the table must be true? Circle the correct answer. No need to show any work. (4 pts) (A) The range is at least 41 but at most 79. (B) The range is at least 41 but at most 120. (C) The range is at least 81 but at most 100. (D) The range is 79. Score Frequency 41-60 3 61-80 8 81-100 12 101-120 7 3. Below are the ages in years for a sample of n = 14 people. Construct a stem and leaf display using the stems shown below with the leaves in order from smallest to largest. (4 pts) 36 23 21 22 27 11 38 13 18 24 10 12 15 25 Stem 1 1 2 2 3 3 Leaf 1
4. Here is a histogram of 301 observations x 1, x 2,..., x 300, x 301 with the exact frequency of each class interval displayed on top of the bin corresponding to it. Fill in the blank or circle the correct answer. No need to show any work. (4 pts total, 2 pts each) (i) The midpoint of the class interval in which the median lies is:. (ii) The distribution of the data set represented by this histogram is: left-skewed / symmetric / right - skewed. 5. Find the mean (2 pts), mode(1 pt), variance (4 pts) and standard deviation (2 pts) of the following sample data set: 1, 2, 5, 5, 7. Write those values in the space provided. (9 pts total) Show all your work in the computation of the mean and the variance. For the variance, you may use the table below if you wish. Mean = Mode = Variance = Stdev. = Value Distance from the Mean Distance Squared from the Mean 2
6. Ten men were weighed on a weighing machine. It showed weights of 120, 124, 125, 126, 128, 132, 134, 135, 136, 140 giving an average of 130 pounds and a standard deviation of 6.34 pounds. It was later found that the machine had a zero error: it showed 2 pounds even when nothing was on the scale. Consequently the correct weights are 118, 122, 123, 124, 126, 130, 132, 133, 134, 138. For the following questions, circle the correct answer. No need to show any work. (4 pts total) i) For the correct weights the mean is (2 pts) (A) 130 (B) 132 (C) 128 (D) none in this list ii) For the correct weights the standard deviation is (2 pts) (A) 8.34 (B) 4.34 (C) 12.68 (D) 6.34 7. The amount of time workers spend commuting to their jobs each day in a large metropolitan city has a mean of 60 minutes and a standard deviation of 20 minutes. Assuming nothing is known about the shape of the distribution of commuting times, what can be said about the proportion of workers who take longer than 2 hours to commute? (6 pts) Circle the correct answer and explain your reasoning clearly. (A) at most 11% (B) at least 89% (C) approximately 0.15% (D) at most 5.5% 8. You score at the 80 th percentile on an exam taken by 700 students. (5 pts total) Answer the following questions giving an integer value not a percentage and showing your work Approximately how many students scored below you? (2 pts) Approximately how many students scored above you? (3 pts) 3
9. Suppose the height of male students at MSU has a symmetric mound shaped distribution with mean 70 and standard deviation 5. For each of the following questions, explain your answer fully either by using sentences or by drawing a graph. (16 pts total) (i) Approximately what proportion of students have a height above 70? (2 pts) (ii) Approximately what proportion of students have a height between 65 and 75? (2 pts) (iii) Approximately what proportion of students have a height between 65 and 85? (4 pts) (iv) Approximately what proportion of students have a height below 60? (4 pts) (v) A height of is approximately the 16th percentile. (4 pts) 4
10. At the U.S. Open Tennis Championship a statistician keeps track of every serve that a player hits during the tournament. The statistician reported that the mean serve speed of a particular player was 100 miles per hour (mph) and the standard deviation of the serve speeds was 8 mph. Find the z-score of each of the following serve speeds and circle whether each of them is an outlier. Clearly write the expression (formula) you use to compute the z-score with the appropriate numbers. (9 pts total, 2 pts for each z-score and 1 pt for each choice of outlier/not) (i) Serve speed: 72 mph z-score = outlier / not an outlier (ii) Serve speed: 108 mph z-score = outlier / not an outlier (iii) Serve speed: 115 mph z-score = outlier / not an outlier 11. A sample of n = 18 gives the following data: -13-10 -3-1 -1 0 1 1 2 3 4 5 5 6 8 11 18 20 Find the following quantities then make the Box Plot using the x-axis shown below. Include the whiskers and the outliers. (16 pts total) (1 pt for IQR, 1 pt for each whisker, 3 pts for outliers, 2 pts for each other quantity) Q 1 = Q 3 = Median = IQR = Lower Fence = Upper Fence = Outliers = -14-12 -10-8 -6-4 -2 0 2 4 6 8 10 12 14 16 18 20 22 5
Extra Credit: A cattle breeder must decide whether to buy a herd consisting of 5000 cows. If 1500 cows weigh at least 1300 pounds, the person will purchase the herd; otherwise, he won t. The current owner of the herd reports that the weight of his cows has a mean of 1000 pounds and a variance of 22500. Based on this information, what is the buyer s decision? Clearly explain your reasoning. Little or no partial credit will be given. (5 pts) 6