Active Learning Lecture Slides For use with Classroom Response Systems Chapter 7: Sampling Distributions Statistics: The Art and Science of Learning from Data Second Edition by Agresti/Franklin

Copyright © 2009 Pearson Education 7.1.1) Suppose that 40% of men over the age of 30 suffer from lower back pain. For a random sample of 50 men over the age of 30, find the mean and the standard error of the sampling distribution of the sample proportion of men over the age of 30 that suffer from lower back pain. Mean = 0.40 Standard Error = 0.0693 Mean= 20 Standard Error = 3.464 Mean = 0.40 Standard Error = 3.464 Mean = 20 Standard Error = 0.0693 e) Cannot be determined Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.1.1) Suppose that 40% of men over the age of 30 suffer from lower back pain. For a random sample of 50 men over the age of 30, find the mean and the standard error of the sampling distribution of the sample proportion of men over the age of 30 that suffer from lower back pain. Mean = 0.40 Standard Error = 0.0693 Mean= 20 Standard Error = 3.464 Mean = 0.40 Standard Error = 3.464 Mean = 20 Standard Error = 0.0693 e) Cannot be determined Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.1.2) Suppose that 40% of men over the age of 30 suffer from lower back pain. For a random sample of 50 men over the age of 30 find the mean and the standard deviation of X (the number of men over the age of 30 that suffer from lower back pain.) Mean = 0.40 Standard Error = 0.0693 Mean = 20 Standard Error = 3.464 Mean = 0.40 Standard Error = 3.464 Mean = 20 Standard Error = 0.0693 e) Cannot be determined Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.1.2) Suppose that 40% of men over the age of 30 suffer from lower back pain. For a random sample of 50 men over the age of 30 find the mean and the standard deviation of X (the number of men over the age of 30 that suffer from lower back pain.) Mean = 0.40 Standard Error = 0.0693 Mean = 20 Standard Error = 3.464 Mean = 0.40 Standard Error = 3.464 Mean = 20 Standard Error = 0.0693 e) Cannot be determined Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.1.3) Suppose that a pre-election poll of 500 people showed that 51% of the sample supported the incumbent senator. If the population proportion who supported the incumbent senator is really 48%, how likely is it that we would see poll results such as this or higher? 0.006 0.03 0.0823 0.0901 0.0968 Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.1.3) Suppose that a pre-election poll of 500 people showed that 51% of the sample supported the incumbent senator. If the population proportion who supported the incumbent senator is really 48%, how likely is it that we would see poll results such as this or higher? 0.006 0.03 0.0823 0.0901 0.0968 Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.1.4) Suppose that 80% of Americans prefer milk chocolate to dark chocolate. Is the sampling distribution of the sample proportion that prefers milk chocolate normally distributed for samples of size 200? Yes, because n is bigger than 30. Yes, because n is bigger than 15. Yes, because np > 15 and n(1-p) > 15. No, because np or n(1-p) is not greater than 15. Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.1.4) Suppose that 80% of Americans prefer milk chocolate to dark chocolate. Is the sampling distribution of the sample proportion that prefers milk chocolate normally distributed for samples of size 200? Yes, because n is bigger than 30. Yes, because n is bigger than 15. Yes, because np > 15 and n(1-p) > 15. No, because np or n(1-p) is not greater than 15. Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.1.5) What is the sampling distribution of the sample proportion if np > 15 and n(1 - p) > 15? a) b) c) d) Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.1.5) What is the sampling distribution of the sample proportion if np > 15 and n(1 - p) > 15? a) b) c) d) Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.2.1) Suppose that you and 100 other people ask 25 randomly selected workers how much money they spent on lunch. Which of the following statements would be true? All samples would result in the same sample mean. All samples would results in slightly difference sample means. Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.2.1) Suppose that you and 100 other people ask 25 randomly selected workers how much money they spent on lunch. Which of the following statements would be true? All samples would result in the same sample mean. All samples would results in slightly difference sample means. Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.2.2) Suppose that you wanted to take a sample of South Carolina elementary school teachers. What impact does using a larger sample size have on the sampling distribution of ? The mean will increase. The mean will decrease. The standard error will increase. The standard error will decrease. Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.2.2) Suppose that you wanted to take a sample of South Carolina elementary school teachers. What impact does using a larger sample size have on the sampling distribution of ? The mean will increase. The mean will decrease. The standard error will increase. The standard error will decrease. Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.2.3) Suppose that South Carolina elementary school teacher salaries have a distribution that is right skewed with a mean of $27,000 and a standard deviation of $2,000. Suppose that someone took a random sample of 40 elementary school teachers salaries and found the sample mean. What is the standard error of ? 2,000 2,000 / 40 Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.2.3) Suppose that South Carolina elementary school teacher salaries have a distribution that is right skewed with a mean of $27,000 and a standard deviation of $2,000. Suppose that someone took a random sample of 40 elementary school teachers salaries and found the sample mean. What is the standard error of ? 2,000 2,000 / 40 Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.2.4) Suppose that the population mean number of hours worked per week for people from Idaho is 40.2 hrs with a population standard deviation of 0.4 hrs. Between what two values will 95% of all sample means from all possible samples of size 40 lie between? (38.94, 41.47) (39.40, 41.00) (40.07, 40.33) (40.14, 40.26) Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.2.4) Suppose that the population mean number of hours worked per week for people from Idaho is 40.2 hrs with a population standard deviation of 0.4 hrs. Between what two values will 95% of all sample means from all possible samples of size 40 lie between? (38.94, 41.47) (39.40, 41.00) (40.07, 40.33) (40.14, 40.26) Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.2.5) For which combination of population and sample size listed below will you find the sampling distribution of the sample mean normally distributed? Population is Right Skewed and n = 10 Population is Right Skewed and n = 40 Population is Bell Shaped and n = 10 B and C only A, B and C Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.2.5) For which combination of population and sample size listed below will you find the sampling distribution of the sample mean normally distributed? Population is Right Skewed and n = 10 Population is Right Skewed and n = 40 Population is Bell Shaped and n = 10 B and C only A, B and C Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.3.1) True or False: For one population distribution there is only one data distribution. True False Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.3.1) True or False: For one population distribution there is only one data distribution. True False Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.3.2) With larger sample sizes there is a greater likelihood that the data distribution… will look similar to the population distribution. will look less like the population distribution. is the same as the sampling distribution of the sample mean. is the same as the sampling distribution of the sample proportion Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.3.2) With larger sample sizes there is a greater likelihood that the data distribution… will look similar to the population distribution. will look less like the population distribution. is the same as the sampling distribution of the sample mean. is the same as the sampling distribution of the sample proportion Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.3.3) The distribution of textbook sales for all college students is right skewed with a mean of $300 and a standard deviation of $120. Suppose that a researcher who didn’t know this information sampled 40 students. She found that the students paid $280 on average with a standard deviation equal to $109. What is the population distribution? Shape: Normal Mean: 300 Stdev: 120 Shape: Approx. Normal Mean: 300 Stdev: Shape: Rt. Skewed Mean: 300 Stdev: 120 Shape: Rt. Skewed Mean: 280 Stdev: 109 Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.3.3) The distribution of textbook sales for all college students is right skewed with a mean of $300 and a standard deviation of $120. Suppose that a researcher who didn’t know this information sampled 40 students. She found that the students paid $280 on average with a standard deviation equal to $109. What is the population distribution? Shape: Normal Mean: 300 Stdev: 120 Shape: Approx. Normal Mean: 300 Stdev: Shape: Rt. Skewed Mean: 300 Stdev: 120 Shape: Rt. Skewed Mean: 280 Stdev: 109 Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.3.4) The distribution of textbook sales for all college students is right skewed with a mean of $300 and a standard deviation of $120. Suppose that a researcher who didn’t know this information sampled 40 students. She found that the students paid $280 on average with a standard deviation equal to $109. What is the data distribution? Shape: Approx. Normal Mean: 300 Stdev: Shape: Most likely Rt. Skewed Mean: 280 Stdev:109 Shape: Most likely Rt. Skewed Mean: 300 Stdev: 120 Shape: Approx. Rt. Skewed Mean: 300 Stdev: Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.3.4) The distribution of textbook sales for all college students is right skewed with a mean of $300 and a standard deviation of $120. Suppose that a researcher who didn’t know this information sampled 40 students. She found that the students paid $280 on average with a standard deviation equal to $109. What is the data distribution? Shape: Approx. Normal Mean: 300 Stdev: Shape: Most likely Rt. Skewed Mean: 280 Stdev:109 Shape: Most likely Rt. Skewed Mean: 300 Stdev: 120 Shape: Approx. Rt. Skewed Mean: 300 Stdev: Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.3.5) The distribution of textbook sales for all college students is right skewed with a mean of $300 and a standard deviation of $120. Suppose that a researcher who didn’t know this information sampled 40 students. She found that the students paid $280 on average with a standard deviation equal to $109. What is the sampling distribution of the sample mean? Shape: Approx. Normal Mean: 300 Stdev: 120 Shape: Approx. Normal Mean: 280 Stdev: 109 Shape: Approx. Normal Mean: 300 Stdev: Copyright © 2009 Pearson Education

Copyright © 2009 Pearson Education 7.3.5) The distribution of textbook sales for all college students is right skewed with a mean of $300 and a standard deviation of $120. Suppose that a researcher who didn’t know this information sampled 40 students. She found that the students paid $280 on average with a standard deviation equal to $109. What is the sampling distribution of the sample mean? Shape: Approx. Normal Mean: 300 Stdev: 120 Shape: Approx. Normal Mean: 280 Stdev: 109 Shape: Approx. Normal Mean: 300 Stdev: Copyright © 2009 Pearson Education