Answered: The nicotine content in cigarettes of 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

The nicotine content in cigarettes of a certain brand is normally distributed. The brand advertises that the mean nicotine content of their cigarettes is µ = 1.5, but measurements on a random sample of 100 cigarettes of this brand gave a mean of ?̅= 1.53 and s = 0.95. Is this evidence that the mean nicotine content is actually higher than advertised?

1. State the appropriate null and alternative hypotheses.

H0: ? = 1.5

Ha: ? > 1.5

2. Should you use the z or t test?

t – do not have sigma

3. Compute the test statistic to test your hypotheses. (report to 2 decimal places)

? = 1.53−1.5 0.95 √100 ⁄ = 0.32

4. Find the appropriate range of p-value for your test. P-value:

a. Less than 0.005

b. Between 0.005 and 0.01

c. Between 0.01 and 0.025

d. Between 0.025 and 0.05

e. Greater than 0.05

Area = 0.05
Area = 0.025
Area = 0.01
Area = 0.005
-1.660
-2.626
-1.984
-2.364
0
+1.660
+1.984
Area = 0.05
Area = 0.025
+2.364
Area = 0.01
Area = 0.005
+2.626

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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