STAT 190, EXAM 1 NAME: DO NOT OPEN THE TEST UNTIL YOU ARE TOLD TO DO SO

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1 STAT 190, EXAM 1 NAME: DO NOT OPEN THE TEST UNTIL YOU ARE TOLD TO DO SO

2 1. ( points each) Determine if each of the underlined value is a parameter or a statistic. (a) We want to learn the average score of this Stat 190 course and we see that this average score is 88. Parameter (b) In a survey, 66.4% of students in the survey use alcohol. Statistic (c) 48.4% of all U.S. residents are men. Parameter (d) We randomly pick 1000 people and see that 48.4 % of them are men. Statistic (e) We want to check if a coin is fair by flipping it 100 times and we get a tail 48 times. Statistic. ( points each) Determine whether the variable is qualitative or quantitative. (a) The number of students at Truman State University. Quantitative (b) The temperature in this room. Quantitative (c) Student ID number. Qualitative (d) The cost of the Stat 190 textbook. Quantitative (e) The number on a car license plate. Qualitative 3. We want to analyze the final grades of a particular Calculus class of 30 students and we obtain the frequency distribution table Grade Number of students (frequency) where 4.0 is an A, 3.0 is a B,.0 is a C, and 1.0 is a D. (a) ( points) Find the mean of the final grades. Show your work (using a statistical calculator to get a quick number is not accepted). The mean is µ = = (b) (4 points) Find the variance and the standard deviation of the grades. Show your work (using a statistical calculator to get a quick number is not accepted). The variance is (4.9) 10 + (3.9) 10 + (.9) 7 + (1.9) The standard deviation is

3 (c) (4 points) Draw a frequency histogram for this problem. distribution. What is the shape of the It is a skewed left distribution. 4. Given the sample below x y Given that x = 5.4, s x.1, ȳ = 8., s y = 3.9. We treat x as a explanatory variable and y as a response variable. (a) (5 points) Compute the linear correlation coefficient r. Show how you use the formula to get the answer. The formula implies that r is (3 5.4)(4 8.) + (4 5.4)(6 8.) + (5 5.4)(7 8.) + (7 5.4)(10 8.) + (8 5.4)(14 8.) (5 1) (b) ( points) Could we have a linear relation between x and y? Are the two variable positively associated or negatively associated? Explain how you have the answers for these two questions. We could have a linear relation between x and y because r is close to 1. It is a positive association because r is positive. (c) (3 points) Find the equation of the least-squares regression line ŷ = b 1 x + b 0. (d) The formulas give and Thus the equation is ŷ = 1.80x 1.5. b = 1.80 b = 1.5. =

4 5. (3 points each) The following data represent the age of 44 U.S. presidents on their inauguration days (a) Find the quartiles: Q 1, Q, Q 3. The quartiles are 4, 43, 46, 46, 47, 47, 48, 49, 49, 50, 50, 51, 51, 51, 51, 5, 5, 54, 54, 54, 54, 54, 55, 55, 55, 55, 56, 56, 56, 57, 57, 57, 57, 58, 60, 61, 61, 61, 6, 64, Q = Q 1 = Q 3 = 64, 65, 68, = 54.5, = 50.5, = (b) Find the interquartile range IQR. The interquartile range is Q 3 Q 1 = = 7. (c) Find the lower and upper fences. The lower fence is and the upper fence is (d) Find any outlier. 69 is an outlier. (e) Draw a boxplot = 40, = 68. 4

5 6. (3 points each) We randomly select random people from a group of 10 people including 7 men and 3 women. (a) What is the probability that both of them are men? Hint: do you see that it is an AND of two events? The probability that the first person is a man AND the second person is a man is = (b) What is the probability that we select at least a woman? Hint: what is the complement of this case? The complement of this event is the case where both of them are men. Thus the answer is = (c) What is the probability that the first person is a man and the second person is a woman? The probability is = (d) What is the probability that the first person is a woman and the second person is a man? The probability is = (e) What is the probability that we select a man and a woman where we do not care who is the first and who is the second? Hint: Do you see that it is an OR of two events? It is either part c OR part d. Since part c and part d are disjoint event, the addition rule gives = The following data represent the number of different communication activities (e.g., cell phone, text messaging, and ) used by a random sample of 400 teenagers in a given week Activities Total Male Female Total (a) (6 points) We want to check if the events male and 0 activities are independent. Follow the following steps: define one event as A and the other as B; find P (B A) and P (B); give a conclusion if the two events are independent with your computations. We note that P (male 0 activities) = 1 4 = 0.5, P (male) = =

6 Thus the two events are independent. (b) (3 points) Are the events male and 0 activities disjoint? Explain why (a yes or no without any explanation will not be accepted). No, because there are 1 men with 0 activities. (c) (6 points) We want to check if the events female and 5-7 activities are independent. Follow the following steps: define one event as A and the other as B; find P (B A) and P (B); give a conclusion if the two events are independent with your computations. Again, we need to check if We note that Thus the two events are not independent. P (female 5-7 activities) = P (female). P (female 5-7 activities) = = 0.65, P (female) = = 0.5. (d) (3 points) Are the events female and 5-7 activities disjoint? Explain why (a yes or no without any explanation will not be accepted). No, because there are 71 women with 5-7 activities. (e) ( points) Are the events 1- activities and 3-4 activities disjoint? Explain why (a yes or no without any explanation will not be accepted). Yes, because we cannot have any person with both 1- activities and 3-4 activities. 8. Using the multiplication counting technique to answer the questions below. (a) (5 points) Four students come into a classroom with 0 chairs. How many ways can they seat? The number of ways is = (b) (5 points) A social security number has the form xxx-xx-xxxx where x is a digit from 0 to 9. How many Social Security numbers can be formed? The number of SSNs is