A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.6; 2.8; 3.1; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) part a Construct a 95% confidence interval for the population mean length of time. (i) State the confidence interval. (Round your answers to two decimal places.) (ii) part b Sketch the graph. a/2 = CL= a/2 = part c iii) Calculate the error bound. (Round your answer to two decimal places.) Part (d What does it mean to be "95% confident" in this problem? This means that the chances of a tranquilizer being effective is 95%. This means that we are 95% confident that the average length of effectiveness of tranquilizers in the sample of 9 people is between the interval values. We are 95% confident that the effectiveness of a tranquilizer lies between the interval values. This means that if intervals are created from repeated samples, 95% of them will contain the true population average length of effectiveness of tranquilizers.

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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A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.6; 2.8; 3.1; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.
NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
part a Construct a 95% confidence interval for the population mean length of time.
(i) State the confidence interval. (Round your answers to two decimal places.)

(ii) part b Sketch the graph.

a/2 =

CL=

a/2 =

part c iii) Calculate the error bound. (Round your answer to two decimal places.)
Part (d
What does it mean to be "95% confident" in this problem?
This means that the chances of a tranquilizer being effective is 95%.
This means that we are 95% confident that the average length of effectiveness of tranquilizers in the sample of 9 people is between the interval values.
We are 95% confident that the effectiveness of a tranquilizer lies between the interval values.
This means that if intervals are created from repeated samples, 95% of them will contain the true population average length of effectiveness of tranquilizers.

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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