One personality test available on the World Wide Web has a subsection designed to assess the "honesty" of the test-taker. You are interested in the mean score,μ, among the general population on this subsection. The website reports thatμis145, but you have good reason to believe thatμis less than145. You decide to do a statistical test. You choose a random sample of people and have them take the personality test. You find that their mean score on the subsection is140and that the standard deviation of their scores is22.Based on this information, complete the parts below.(a)What are the null hypothesisH0and the alternative hypothesisH1that should be used for the test?H0:H1:(b)Suppose that you decide not to reject the null hypothesis. What sort of error might you be making? ▼(Choose one) (c)Suppose the true mean score among the general population on the subsection is137. Fill in the blanks to describe a Type II error.A Type II error would be ▼(Choose one) the hypothesis thatμis ▼(Choose one)▼(Choose one) when, in fact,μis ▼(Choose one) .

The test is to check whether the population mean is less than 145.

Answered: One personality test available on the…

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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One personality test available on the World Wide Web has a subsection designed to assess the "honesty" of the test-taker. You are interested in the mean score,

, among the general population on this subsection. The website reports that

145

, but you have good reason to believe that

is less than

145

. You decide to do a statistical test. You choose a random sample of people and have them take the personality test. You find that their mean score on the subsection is

140

and that the standard deviation of their scores is

Based on this information, complete the parts below.

(a)	What are the null hypothesis H0 and the alternative hypothesis H1 that should be used for the test?
H0:
H1:
(b)	Suppose that you decide not to reject the null hypothesis. What sort of error might you be making?
	▼(Choose one)
(c)	Suppose the true mean score among the general population on the subsection is 137 . 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)▼(Choose one) when, in fact, μ is ▼(Choose one) .

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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