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Active Learning Lecture Slides For use with Classroom Response Systems Chapter 12: Confidence Intervals and Hypothesis Tests for Means Business Statistics First Edition by Sharpe, De Veaux, Velleman Copyright © 2010 Pearson Education, Inc. Slide 10- 1 Which of the following is not an assumption or condition that needs to be checked to construct a confidence interval for the mean using the Student’s t distribution? A. Randomization B. 10% Condition C. Success/Failure Condition D. Nearly Normal Condition Copyright © 2010 Pearson Education, Inc. Slide 12- 2 Which of the following is not an assumption or condition that needs to be checked to construct a confidence interval for the mean using the Student’s t distribution? A. Randomization B. 10% Condition C. Success/Failure Condition D. Nearly Normal Condition Copyright © 2010 Pearson Education, Inc. Slide 12- 3 Which statement correctly compares t-distributions to the normal distribution? I. t distributions and the Normal are symmetric. II. t distributions have less spread than the Normal distribution. III. t distributions and the Normal are bell shaped. A. I only B. II only C. I and II only D. I and III only Copyright © 2010 Pearson Education, Inc. Slide 12- 4 Which statement correctly compares t-distributions to the normal distribution? I. t distributions and the Normal are symmetric. II. t distributions have less spread than the Normal distribution. III. t distributions and the Normal are bell shaped. A. I only B. II only C. I and II only D. I and III only Copyright © 2010 Pearson Education, Inc. Slide 12- 5 Which of the following is true about Student’s t-models? A. They are unimodal and symmetric. B. They have fatter tails than the Normal model. C. As the degrees of freedom increase, the tmodels look more and more like the Normal Model D. All of the above. Copyright © 2010 Pearson Education, Inc. Slide 12- 6 Which of the following is true about Student’s t-models? A. They are unimodal and symmetric. B. They have fatter tails than the Normal model. C. As the degrees of freedom increase, the tmodels look more and more like the Normal Model D. All of the above. Copyright © 2010 Pearson Education, Inc. Slide 12- 7 A researcher found that a 98% confidence interval for the mean hours per week spent studying by college students was (13, 17). Which is true? A. There is a 98% chance that the mean hours per week spent studying by college students is between 13 and 17 hours. B. We are 98% sure that the mean hours per week spent studying by college students is between 13 and 17 hours. C. Students average between 13 and 17 hours per week studying for 98% of the weeks. D. 98% of all students spend between 13 and 17 hours studying per week. Copyright © 2010 Pearson Education, Inc. Slide 12- 8 A researcher found that a 98% confidence interval for the mean hours per week spent studying by college students was (13, 17). Which is true? A. There is a 98% chance that the mean hours per week spent studying by college students is between 13 and 17 hours. B. We are 98% sure that the mean hours per week spent studying by college students is between 13 and 17 hours. C. Students average between 13 and 17 hours per week studying for 98% of the weeks. D. 98% of all students spend between 13 and 17 hours studying per week. Copyright © 2010 Pearson Education, Inc. Slide 12- 9 The owner of small specialty store was interested in the amount customers spent on designs from a local artist. From a random sample of 20 customers, she found a mean of $375 with a standard deviation of $56. To construct a 95% confidence interval for the true mean amount spent, she would use a t value of A. 1.729 B. 2.093 C. 1.96 D. 3.078 Copyright © 2010 Pearson Education, Inc. Slide 12- 10 The owner of small specialty store was interested in the amount customers spent on designs from a local artist. From a random sample of 20 customers, she found a mean of $375 with a standard deviation of $56. To construct a 95% confidence interval for the true mean amount spent, she would use a t value of A. 1.729 B. 2.093 C. 1.96 D. 3.078 Copyright © 2010 Pearson Education, Inc. Slide 12- 11 A professor was curious about her students’ grade point averages (GPAs). She took a random sample of 15 students and found a mean GPA of 3.01 with a standard deviation of 0.534. Which of the following formulas gives a 99% confidence interval for the mean GPA of the professor’s students? A. 3.01± 2.947 0.534 15 0.534 B. 3.01± 2.977 15 C. 3.01± 2.576 0.534 15 D. 3.01± 2.947 0.534 14 Copyright © 2010 Pearson Education, Inc. Slide 12- 12 A professor was curious about her students’ grade point averages (GPAs). She took a random sample of 15 students and found a mean GPA of 3.01 with a standard deviation of 0.534. Which of the following formulas gives a 99% confidence interval for the mean GPA of the professor’s students? A. 3.01± 2.947 0.534 15 0.534 B. 3.01± 2.977 15 C. 3.01± 2.576 0.534 15 D. 3.01± 2.947 0.534 14 Copyright © 2010 Pearson Education, Inc. Slide 12- 13 A coffee house owner knows that customers pour different amounts of coffee into their cups. She samples cups from 10 costumers she believes to be representative of the customers and weighs the cups, finding a mean of 12.5 ounces and standard deviation of 0.5 ounces. Which of the following formulas gives a 95% confidence interval for the mean weight of all cups of coffee? A. 12.5 ± 1.96 0.5 10 B. 12.5 ± 2,228 0.5 10 C. 12.5 ± 2.262 0.5 10 D. 12.5 ± 2.262 0.5 9 Copyright © 2010 Pearson Education, Inc. Slide 12- 14 A coffee house owner knows that customers pour different amounts of coffee into their cups. She samples cups from 10 costumers she believes to be representative of the customers and weighs the cups, finding a mean of 12.5 ounces and standard deviation of 0.5 ounces. Which of the following formulas gives a 95% confidence interval for the mean weight of all cups of coffee? A. 12.5 ± 1.96 0.5 10 B. 12.5 ± 2,228 0.5 10 C. 12.5 ± 2.262 0.5 10 D. 12.5 ± 2.262 0.5 9 Copyright © 2010 Pearson Education, Inc. Slide 12- 15 After instituting some improvements, a bank wished to test whether service times at the drive through window improved. The average service time had been 110 seconds. A sample of 25 customers resulted in a mean of 100 seconds with a standard deviation of 40 seconds. Which hypotheses should they test? A. H0: µ < 110 HA: µ > 110 B. H0: µ = 110 HA: µ > 110 C. H0: µ > 100 HA: µ = 100 D. H0: µ = 110 HA: µ < 110 Copyright © 2010 Pearson Education, Inc. Slide 11- 16 After instituting some improvements, a bank wished to test whether service times at the drive through window improved. The average service time had been 110 seconds. A sample of 25 customers resulted in a mean of 100 seconds with a standard deviation of 40 seconds. Which hypotheses should they test? A. H0: µ < 110 HA: µ > 110 B. H0: µ = 110 HA: µ > 110 C. H0: µ > 100 HA: µ = 100 D. H0: µ = 110 HA: µ < 110 Copyright © 2010 Pearson Education, Inc. Slide 11- 17 After instituting some improvements, a bank wished to test whether service times at the drive through window improved. The average service time had been 110 seconds. A sample of 25 customers resulted in a mean of 100 seconds with a standard deviation of 40 seconds. What is the value of the calculated t statistic? A. -1.25 B. 0.25 C. 2.75 D. -2.35 Copyright © 2010 Pearson Education, Inc. Slide 11- 18 After instituting some improvements, a bank wished to test whether service times at the drive through window improved. The average service time had been 110 seconds. A sample of 25 customers resulted in a mean of 100 seconds with a standard deviation of 40 seconds. What is the value of the calculated t statistic? A. -1.25 B. 0.25 C. 2.75 D. -2.35 Copyright © 2010 Pearson Education, Inc. Slide 11- 19 After instituting some improvements, a bank wished to test whether service times at the drive through window improved. The average service time had been 110 seconds. A sample of 25 customers resulted in a mean of 100 seconds with a standard deviation of 40 seconds. What can we conclude? A. The mean service time increased. B. The mean service time did not decrease. C. The test is inconclusive. D. The mean service time decreased. Copyright © 2010 Pearson Education, Inc. Slide 11- 20 After instituting some improvements, a bank wished to test whether service times at the drive through window improved. The average service time had been 110 seconds. A sample of 25 customers resulted in a mean of 100 seconds with a standard deviation of 40 seconds. What can we conclude? A. The mean service time increased. B. The mean service time did not decrease. C. The test is inconclusive. D. The mean service time decreased. Copyright © 2010 Pearson Education, Inc. Slide 11- 21