Answered: Suppose you are a researcher in a…

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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Question

Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You collect data from a random sample of 11 patients. The period of effectiveness of the tranquilizer for each patient (in hours) is as follows:

2.2
2.1
2.2
2.1
2.3
2
2.8
2.5
2.7
2.7
2.7

a. What is a point estimate for the population mean length of time. (Round answer to 4 decimal places)

b. Which distribution should you use for this problem?

normal distribution
t-distribution

c. Why?

d. What must be true in order to construct a confidence interval in this situation?

The population must be approximately normal
The sample size must be greater than 30
The population mean must be known
The population standard deviation must be known

e. Construct a 80% confidence interval for the population mean length of time. Enter your answer as an open-interval (i.e., parentheses) Round upper and lower bounds to two decimal places

f. Interpret the confidence interval in a complete sentence. Make sure you include units

g. What does it mean to be "80% confident" in this problem? Use the definition of confidence level.

There is a 80% chance that the confidence interval contains the population mean
The confidence interval contains 80% of all samples
80% of all simple random samples of size 11 from this population will result in confidence intervals that contain the population mean

h. Suppose that the company releases a statement that the mean time for all patients is 2 hours.

Is this possible?

Is it likely?

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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