A psychologist has designed an index to measure the social perspectives of elementary school children. The index is based on ratings of a child’s responses to questions about a set of photographs showing different social situations. The following are the indices measured on a random sample of 16 children attending elementary school in a particular district. 48, 75, 69, 58, 60, 68, 59, 66, 71, 52, 49, 60, 54, 55, 70, 57 For the data the mean index is 60.69 and the standard deviation is 8.26.Perform a statistical test to determine if the population mean index is greater than 50.a) Name of hypothesis test: b) H0: c) HA: d) Test Statistic: e) Rejection region: f) Decision in the context of the problem:

For the given data Find all the required

Answered: A psychologist has designed an index to…

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 has designed an index to measure the social perspectives of elementary school children. The index is based on ratings of a child’s responses to questions about a set of photographs showing different social situations. The following are the indices measured on a random sample of 16 children attending elementary school in a particular district.

48, 75, 69, 58, 60, 68, 59, 66, 71, 52, 49, 60, 54, 55, 70, 57

For the data the mean index is 60.69 and the standard deviation is 8.26.

Perform a statistical test to determine if the population mean index is greater than 50.

a) Name of hypothesis test:

b) H₀:

c) H_A:

d) Test Statistic:

e) Rejection region:

f) Decision in the context of the problem:

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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