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.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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