Answered: psychologist is studying the self image…

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

psychologist is studying the self image of smokers, as measured by the self-image (SI) score from a personality inventory. She would like to examine the mean SI score, u, for the population of all smokers. Previously published studies have indicated that the mean SI score for the population of all smokers is 80 and that the standard deviation is 12, but the psychologist has good reason to believe that the value for the mean has changed. She plans to perform a statistical test. She takes a random sample of SI scores for smokers and computes the sample mean to be 72 Based on this information, complete the parts below.

A psychologist is studying the self image of smokers, as measured by the self-image (SI) score from a personality inventory. She would
like to examine the mean SI score, u, for the population of all smokers. Previously published studies have indicated that the mean SI
score for the population of all smokers is 80 and that the standard deviation is 12, but the psychologist has good reason to believe that
the value for the mean has changed. She plans to perform a statistical test. She takes a random sample of SI scores for smokers and
computes the sample mean to be 72.
Based on this information, complete the parts below.
(a) What are the null hypothesis H and the alternative hypothesis H₁ that should be used for
μ
the test?
O<O
Ho
:
H₁ : 0
(b) Suppose that the psychologist decides to reject the null hypothesis. What sort of error might
X
she be making?
(Choose one)
(c) Suppose the true mean SI score for all smokers is 68. Fill in the blanks to describe a Type II
error.
A Type II error would be (Choose one)
the hypothesis that μ is
(Choose one)
when, in fact, μu is (Choose one)
(Choose one)
ロミロ
XI
OSO
0=0 0#0
?

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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