Midterm exam practice PDF

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Name Statistics 10XL – Spring 2019 Midterm Test No. 1 You may not use your cell phone as a calculator during the exam. Fill out a new scantron if you leave eraser marks. Grading errors on scantron will not be manually reviewed. Show work where required or exam may not be accepted. No leaving room during exam. (1) The number of votes a presidential candidate receives is an example of a: (a) Response variable (b) Categorical variable (c) Confounding variable (d) Numerical variable (2) Which of the following measurements is likely to have the least variation (i.e. which dataset would have the smallest standard deviation)? (a) The circumferences of quarters from a roll of quarters. (b) The SAT scores of a class of graduating high school seniors. (c) The individual heights of children, measured in inches, in a randomly selected class of sixth grade students. (d) The miles per gallon in a randomly selected sample of cars from the 405 freeway. (3) The mean sales prices for a sample of homes in some city was $1,250,000. The median sales price of these same homes was $1,250,000. The distribution of home sale prices in this city is: (a) Right-skewed (b) Bimodal (c) Left-skewed (d) Symmetric (4) Curious about the effect of exercise on preventing the common cold, a researcher collects data from a sample of people on total hours of exercise and number of colds had in the past year. This is an example of: (a) Linear regression (b) Controlled experiment (c) Observational study (d) Independence

Use the following sample of seven randomly selected peoples' ages to answers questions (5) - (7). 37

51

53

35

45

38

81

(5) What is the median age? (a) 35 (b) 45 (c) 51 (d) 37 (6) What is the IQR of the data? (a) 13 (b) 81 (c) 16 (d) 22 (7) Using the upper and lower fences definition of outlier, do we have any outliers in the age sample data? Show work here.

(a) An outlier above the upper fence (b) An outlier below the lower fence (c) Outliers beyond both fences (d) No outliers (8) Bowling balls from Southern California bowling alleys have a mean weight of 12 pounds with a standard deviation of 1.5 pounds. What is the z-score for a ball weighing 9 pounds? (a) +1 (b) -1 (c) +2 (d) -2

Use the following information to answer questions (9) - (11). The mean weight of all Sumo wrestlers is 400 lbs with a standard deviation of 25 lbs. Assume the distribution of Sumo wrestler weights is unimodal and symmetric and so the Empirical Rule applies. (9) What percent of Sumo wrestlers weigh between 400 and 425 lbs? (a) 34% (b) 47.5% (c) 13.5% (d) 81.5% (10) Between what two values would you expect to find the middle 95% of Sumo wrestler weights? (a) 300 to 350 lbs. (b) 350 to 400 lbs. (c) 350 to 450 lbs. (d) 300 to 400 lbs. (11) What percent of Sumo wrestlers weigh more than 375 pounds? (a) 84% (b) 34% (c) 13.5% (d) 95% (12) Which of the following statements regarding the correlation coefficient (r) is true? (a) The correlation coefficient's range is 0.0 to 1.0. (b) A correlation of +1 means that as one variable increases the other decreases. (c) A correlation of -1 means that as one variable increases the other decreases. (d) A value of 0.00 indicates that two variables are perfectly linearly correlated. (13) A positive correlation between variables means our linear regression model will have a positive slope. (a) True (b) False (c) We cannot tell the sign of the slope from the correlation

Use the following information to answer questions (14) - (17). The following linear regression model can be used to predict number of popsicles sold based on the day's temperature:  Sold=500+ 10×( Temperature in ° F ) Popsicles (14) What is the predicted number of popsicles sold if the temperature is 90 °F? (Assume extrapolation is not a concern) (a) 500 popsicles (b) 1,300 popsicles (c) 1,350 popsicles (d) 1,400 popsicles (15) Choose the statement that best states the meaning of the slope in this context. (a) The slope tells us the data had a negative correlation. (b) As the temperature increases by one degree fahrenheit, we expect popsicle sales to increase by 10. (c) The slope tells us that the data was not linear when viewing a scatterplot. (d) We predict sales of 500 popsicles when it is 0 degrees temperature. (16) For a temperature of 100°F, the predicted number of popsicles sold is 1,500. Assume today's temperature was exactly 100°F and 2,000 popsicles were actually sold. Compute the residual for today's prediction. (a) 200 (b) 500 (c) -500 (d) -200 (17) What percent of the variation in popsicles sold can be explained by variations in temperature? (a) 80% (b) 100% (c) 64% (d) 10%

Use the following information to answer questions (18) - (19). In a sample of 32 cars reviewed by Motor Trend magazine, the mean horsepower (hp) was 125 hp with a standard deviation of 15 hp. The mean gas mileage (mpg) is 30 mpg with a standard deviation of 8 mpg. Assume the relationship between mpg and hp is linear and has a correlation of -0.90. This means as hp increases, mpg tends to decrease. (18) What is the slope of the linear regression model predicting gas mileage (y-variable) from horsepower (x-variable)? Show work here.

(a) -0.90 (b) -0.07 (c) -0.48 (d) -0.15 (19) What is the intercept of the linear regression model predicting gas mileage (y-variable) from horsepower (x-variable)? Show work here.

(a) 47.5 (b) 90 (c) 34 (d) 30

(20) 40% of Skittles candies in a bag are red. If you randomly draw 3 Skittles out of the bag what is the probability at least one of them is red? Assume the draws are independent and the probability of red is constant. Show work here.

(a) 0.78 (b) 0.60 (c) 0.12 (d) 0.67 (21) 15% of Skittles candies in a bag are green. If you randomly draw 3 Skittles out of the bag what is the probability the first one is green and the next two are not? Assume the draws are independent and the probability of green is constant. Show work here.

(a) 11% (b) 85% (c) 22% (d) 67%

The following table contains data on two categorical variables recorded from a sample of 189 students. Each student was asked their grade level and their preferred pet. Use for questions (22) - (25). You may want to fill in column and row totals before answering. Preferred Pet Grade Level

Bird

Cat

Dog

Fish

7th Graders

9

27

42

3

8th Graders

12

36

56

4

(22) Given that a student is in the 7th grade, what is the probability their preferred pet is a bird? (a) 52% (b) 27% (c) 11% (d) 33% (23) What is the probability a randomly chosen student is an 8th grader and prefers a dog as a pet? (a) 75% (b) 30% (c) 6% (d) 52% (24) What is the probability a randomly chosen student is an 8th grader or prefers a dog as a pet? (a) 19% (b) 62% (c) 46% (d) 79% (25) Are 'grade level' and 'preferred pet' independent variables? (a) Yes (b) No (c) Cannot tell from the data...