A major American pharmaceutical company has randomly sampled 14 customers who have had prescriptions for one of their new pain killing drugs for 2 months. There is concern that the drug may elevate the user’s heart rate. Each of the customers in the sample had his or her heart rate measured after using the drug for 1 week. All people in the sample had heart rates of 55 prior to taking the drug. The following data were recorded for the 14 customers: 50 70 60 70 90 72 50 80 85 55 66 70 80 40 a. Suppose that you have just started working in the marketing department of the pharmaceutical company. You were given the following instructions: “Based on these sample data construct a 97.5% confidence interval estimate for the true mean heart rate for the company’s drug customers. Interpret the estimate.” Assume that heart rates are normally distributed. b. Referring to your answer in part a, could the estimate be applied to all potential drug customers? Explain why or why not. c. Refer to your calculations in part a. Was the concern expressed justified? Justify your answer. If you conclude the average heart rate did not increase, determine the probability that a sample mean at least as large as the one obtained in your sample could actually have been obtained.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 27PPS

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9. A major American pharmaceutical company has randomly sampled 14 customers who have had prescriptions for one of their new pain killing drugs for 2 months. There is concern that the drug may elevate the user’s heart rate. Each of the customers in the sample had his or her heart rate measured after using the drug for 1 week. All people in the sample had heart rates of 55 prior to taking the drug. The following data were recorded for the 14 customers: 50 70 60 70 90 72 50 80 85 55 66 70 80 40

a. Suppose that you have just started working in the marketing department of the pharmaceutical company. You were given the following instructions: “Based on these sample data construct a 97.5% confidence interval estimate for the true mean heart rate for the company’s drug customers. Interpret the estimate.” Assume that heart rates are normally distributed.

b. Referring to your answer in part a, could the estimate be applied to all potential drug customers? Explain why or why not.

c. Refer to your calculations in part a. Was the concern expressed justified? Justify your answer. If you conclude the average heart rate did not increase, determine the probability that a sample mean at least as large as the one obtained in your sample could actually have been obtained.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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