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Name: A psychologist is studying smokers' self-images, which she measures by
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Description: A psychologist is studying smokers' self-images, which she measures by the self-image (SI) score from a personality inventory. For adults in the U.S., the mean SI score from this inventory is about 145 The psychologist gathers a random sample of 9 SI

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 psychologist is studying smokers' self-images, which she measures by the self-image (SI) score from a personality inventory. For adults in the U.S., the mean SI score from this inventory is about 145 The psychologist gathers a random sample of 9 SI scores of smokers and finds that their mean is 180 and their standard deviation is 36. Assume that the population of SI scores of smokers is normally distributed with mean μ. Based on the sample, can the psychologist conclude that μ is different from 145 ? Use the 0.05 level of significance.

Perform a two-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places and round your answers as specified in the table

(a)	State the null hypothesis H0? and the alternative hypothesis H1? .
H0: ?
H1: ?
(b)	Determine the type of test statistic to use.
	▼(Choose one) z ? t ? chi square? f ?
(c)	Find the value of the test statistic.? (Round to three or more decimal places.)

(d)	Find the two critical values.? (Round to three or more decimal places.)
and
(e)	At the 0.05 level of significance, can the psychologist conclude that the mean SI score among smokers is different from 145 ? yes or no ?
Yes No

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 + ...

Expert Solution

Step 1

Given:

Sample size, n =9

Mean, $μ$ =145

Sample mean, $x$ =180

Standard deviation, $σ$ =36

Level of significance = 0.05

(a) Hypothesis:

Null hypothesis: $H_{0} : μ = 145$

Alternative hypothesis: $H_{a} : μ \neq 145$

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