Answered: What is the F critical value?

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

A college administrator wants to know if there is a significant difference between sexual orientation and level of family support for students at their college. The administrator takes a random sample of students who identify as gay/lesbian, bisexual or heterosexual/straight. There were 22 students sampled in each category. A measure of family support is given with higher scores indicating more family support. The means are as follows:

Gay/lesbian	Bisexual	Heterosexual/Straight
M_G/L = 16	M_Bi = 17	M_H/S = 22

Source	SS	df	MS	F
Orientation	300
Error	2961
Total

What is the F critical value?

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: Determine the given data in the question

Here the the groups are given as,

Gay/lesbian,

Bisexual or

Heterosexual/straight.

Let $mu subscript 1 comma mu subscript 2 space a n d space mu subscript 3$ are the population means for gay/lesbian, bisexual, and heterosexual/straight respectively.

Given that,

$N u m b e r space o f space s t u d e n t s space left parenthesis n right parenthesis equals 22 N o. space o f space f a c t o r s space left parenthesis k right parenthesis equals 3 M subscript G divided by L end subscript equals 16 M subscript B i end subscript equals 17 M subscript H divided by S end subscript equals 22 S S O r i e n t a t i o n equals 300 S S e r r o r equals 2961$

Assume the level of significance $left parenthesis alpha right parenthesis equals 0.05$