Survey

* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project

Survey

Document related concepts

Transcript

Name ________________________ AP Statistics Date _____________ Schwimmer Midterm Review #1 1. A volunteer for a mayoral candidate’s campaign periodically conducts polls to estimate the proportion of people in the city who are planning to estimate the proportion of people in the city who are planning to vote for this candidate in the upcoming election. Two weeks before the election, the volunteer plans to double the sample size in the polls. The main purpose of this is to (1) (2) (3) (4) (5) 2. Which one of the following would be a correct interpretation if you have a z-score of +2.0 on an exam? (1) (2) (3) (4) (5) 3. reduce nonresponse bias reduce the effects of confounding variables reduce bias due to the interviewer effect decrease the variability in the population decrease the standard deviation of the sampling distribution of the sample proportion It means that you missed two questions on the exam. It means that you got twice as many questions correct as the average student. It means that your grade was two points higher than the mean grade on this exam. It means that your grade was in the upper 2% of all grades on this exam. It means that your grade is two standard deviations above the mean for this exam. The statistics below provide a summary of the distribution of heights, in inches, for a simple random sample of 200 young children. Mean: 46 inches Median: 45 inches Standard Deviation: 3 inches First Quartile: 43 inches Third Quartile: 48 inches About 100 children in the sample have heights that are (1) (2) (3) (4) (5) Less than 43 inches Less than 48 inches Between 43 and 48 inches Between 40 and 52 inches More than 46 inches 4. z Jay = Jay, James, and Joe each drive different types of cars. The price they paid for their cars are in the table below along with the mean and standard deviation of the type of car they drive. Show necessary work to determine who paid the most and least amount for their cars relative to their type. Assume that prices for each type are normally distributed. 24857 − 21335 = 1.435 2455 z James = 37925 − 32853 = 1.248 4065 z Joe = 55290 − 48936 = 1.124 5654 Jay paid the most relative to his car type and Joe paid the least relative to his car type. A least squares regression line was fitted to the weights (in pounds) versus age (in months) of a group of many young children. The equation of the line is yˆ = 16.6 + 0.65t , where ŷ is the predicted weight and t is the age of the child. A 20-month old child in this group has an actual weight of 25 pounds. Which of the following is the residual weight, in pounds, for this child? yˆ = 16.6 + 0.65(20) = 29.6 (1) (2) (3) (4) (5) 5. –7.85 –4.60 4.60 5.00 7.85 residual = observed − predicted residual = 25 − 29.6 = −4.6 Let X represent a random variable whose distribution is Normal, with a mean of 100 and a standard deviation of 10. Which of the following is equivalent to P ( X > 115) ? (1) P ( X < 115 ) (2) P ( X ≤ 115 ) (3) P ( X < 85 ) (4) P ( 85 < X < 115) (5) 1 − P ( X < 85 ) 6. The following table shows the federal debt for a short period of time from 1980 through 1991. 3.6 2.8 2.0 1.2 .4 1980 1984 1988 1992 Year (a) Construct a scatterplot on the grid provided. (b) Determine if the data is linear or exponential and explain how you reached your conclusion. After find the equation for the least squares regression line, I constructed a residuals plot. There was an clear pattern, which means a linear model may not be best. After transforming ( ) the data, a scatterplot of (year, log federalˆ debt ) looks linear with an r-value of .9959 and small residuals. (c) Perform exponential regression and generate an equation that predicts the federal debt based on the year. ( ) log federalˆ debt = −110.6417 + .0559(year) (d) Find the residual for this model for the year 1990. ( ) log ( federalˆ debt ) = .5993 log federalˆ debt = −110.6417 + .0559(1990) 10 ( log federalˆ debt ) = 10.5993 federalˆ debt = 3.975 residual = observed – predicted = 3.2 – 3.975 = –.775 (e) Use this model to predict the national debt for the year 2000. ( ) log ( federalˆ debt ) = 1.1583 log federalˆ debt = −110.6417 + .0559(2000) 10 ( log federalˆ debt ) = 101.1583 federalˆ debt = 14.3979 7. “You’ll never have as many friends in your life as you do in high school.” A statistician decides to test the accuracy of this statement so he conducts a long-range study. He starts with 1,000 high school seniors, and asks them to count how many “friends” they have. Every year for 15 years, he stays in touch with the students via email and asks them to inform him how many friends they have. The statistician averages the number of friends per year and 15 years later, plots the points (age, friends). The least squares regression line is: a. The direction of the association is ˆ friends = 116.14 − 2.94(age) b. (1) Positive (2) Negative (3) Impossible to tell c. How can you interpret the equation? A 20 year old is predicted to have (1) 75 friends (2) 57 friends (3) Impossible to tell The strength of the direction is (1) Very strong (2) Moderately strong (3) Moderately weak d. What is the correct interpretation? (1) A person loses 58% of his friends over time. (2) 58% of the variation in ages of people can be explained by the LSRL. (3) 58% of the variation in the number of friends can be explained by the linear relationship of age on friends. (4) 58% of the time we can predict the number of friends a person will lose. (1) For every friend that a person loses, he/she ages about 2.94 years. (2) For every 2.94 years a person ages, he/she loses a friend. (3) For every year a person ages, he/she loses about 2.94 friends. e. r 2 = .58 f. 30 year olds in the study have, on average, 25 friends. What is the residual to the nearest whole number? (1) 3 (2) –3 (3) –5 g. At what age does the model suggest you will only have 25 friends? h. At 39 years old, the prediction is (1) You will only have 1 friend (2) You won’t have any friends. (3) It’s difficult to determine how many friends you’ll have. (1) 31 (2) 43 (3) Impossible to tell 8. The length of time an alkaline AA battery is usable in a CD player is described by a normal distribution with mean of 76.3 hours with a standard deviation of 2.1 hours. For each question, draw a small diagram and answer the question. a. What percentage of batteries get over 80 hours of use? 80 − 76.3 P ( x > 80 ) = P z > = 2.1 P ( z > 1.762 ) = .0390 c. What percentage of batteries gets between 73 and 77 hours of use? 77 − 76.3 73 − 76.3 P ( 73 < x < 77 ) = P z> = 2.1 2.1 P ( −1.571 < z < .3333) = .5725 b. What percentage of batteries get under 75 hours of use? 75 − 76.3 P ( x < 75 ) = P z < = 2.1 P ( z < .61905 ) = .2679 d. A battery getting 78 hours of use would be in what percentile? 78 − 76.3 P ( x < 78 ) = P z < = 2.1 P ( z < .8095) = .7908 79th percentile e. How many hours of use would a battery need to be in the top 10 percentile? f. How many hours of use would a batter need to be in the 99.99th percentile? z = 1.28 z = 3.719 x − 76.3 2.1 78.988 ≈ 79 hours x − 76.3 2.1 84.1099 hours 1.28 = 3.719 = g. Find Q1. h. Find Q3. 25th percentile 75th percentile z = −.6745 z = .6745 x − 76.3 2.1 74.88 hours −.6745 = x − 76.3 2.1 77.72 hours .6745 =