Ap Statistics Chapter 3 Test

Ap Statistics Chapter 3 Test AP Statistics Chapter 3 Test Exploring Data Distributions Instructions This test is designed to assess your understanding of the concepts covered in Chapter 3 of your AP Statistics textbook Show all work for full credit Partial credit may be awarded where applicable You may use a calculator but you must show all steps in your calculations Please circle your final answers Multiple Choice 1 point each 1 Which of the following is NOT a characteristic of a normal distribution a Symmetrical b Bellshaped c Unimodal d Skewed to the right e Mean median and mode are equal 2 A researcher is studying the heights of adult males in a certain country She collects data on a random sample of 100 men Which of the following would be the most appropriate way to display the distribution of the heights a Bar chart b Pie chart c Histogram d Scatterplot e Box plot 3 The standard deviation of a data set measures a The average value of the data b The spread of the data around the mean c The distance between the highest and lowest values d The number of data points in the set e The probability of a particular value occurring 4 A zscore represents 2 a The number of standard deviations a data point is from the mean b The probability of a data point occurring c The difference between the mean and a data point d The median of a data set e The range of a data set 5 Which of the following is TRUE about the empirical rule a It applies to all distributions b It states that approximately 68 of the data falls within one standard deviation of the mean c It is only useful for skewed distributions d It states that approximately 95 of the data falls within two standard deviations of the median e It is used to calculate the probability of a specific event occurring Free Response Points as indicated 1 5 points A study of the amount of sleep college students get each night found that the average amount of sleep was 72 hours with a standard deviation of 15 hours Assume the distribution of sleep times is approximately normal a What is the probability that a randomly selected college student gets less than 6 hours of sleep b What is the probability that a randomly selected college student gets between 8 and 9 hours of sleep c What is the 90th percentile for sleep time 2 5 points The following data represents the number of hours spent studying for an exam by a group of 10 students 3 4 5 6 6 7 7 8 9 10 a Calculate the mean and standard deviation of the data b Create a stemandleaf plot of the data c Describe the shape of the distribution 3 5 points A company that manufactures light bulbs claims that the average life of their bulbs is 1000 hours with a standard deviation of 100 hours A consumer group wants to test this claim by randomly selecting 50 bulbs and testing them 3 a What is the expected value of the mean life of the 50 bulbs b What is the standard error of the mean c Assuming the companys claim is true what is the probability that the sample mean life of the 50 bulbs will be less than 980 hours 4 5 points A researcher wants to study the relationship between the number of hours spent studying and the grade on an exam She collects data from a sample of 20 students a What type of graph would be most appropriate to display the relationship between these two variables b Describe what the researcher should look for in the graph to determine if there is a linear relationship between the two variables c What is the correlation coefficient and what does it tell us about the relationship between the two variables Answer Key Multiple Choice 1 d Skewed to the right 2 c Histogram 3 b The spread of the data around the mean 4 a The number of standard deviations a data point is from the mean 5 b It states that approximately 68 of the data falls within one standard deviation of the mean Free Response 1 5 points a z 6 72 15 08 PX 6 PZ 08 02119 b z1 8 72 15 053 z2 9 72 15 12 P8 X 9 P053 Z 12 02292 c Find the zscore corresponding to the 90th percentile z 128 x 72 128 15 912 hours 2 5 points 4 a Mean 63 hours Standard deviation 202 hours b Stemandleaf plot 0 3 4 0 5 6 6 0 7 7 8 9 1 0 c The distribution is slightly skewed to the right 3 5 points a Expected value of the mean 1000 hours b Standard error of the mean 100 sqrt50 1414 hours c z 980 1000 1414 141 PX 980 PZ 141 00793 4 5 points a Scatterplot b The researcher should look for a linear pattern in the scatterplot If the points tend to form a straight line then there is a linear relationship If the points are scattered randomly then there is no linear relationship c The correlation coefficient measures the strength and direction of the linear relationship between two variables It ranges from 1 to 1 A correlation coefficient of 1 indicates a perfect positive linear relationship while a correlation coefficient of 1 indicates a perfect negative linear relationship A correlation coefficient of 0 indicates no linear relationship Note This is a sample test The actual test may vary in content and format It is important to consult your textbook and class notes for specific information on Chapter 3 topics