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?

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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