Question

An SRS produced the following data. Is browser choice and grade level independent? The responses were categorized below. Test at the .05 significance level. (α = .05)

	Safari	Firefox	Chrome
Freshmen	20	25	40
Sophomore	40	30	30
Junior	50	25	50
Senior	90	20	75

What is your conclusion in plain English?

a) There is not enough evidence to suggest that browser choice and grade level are dependent.

b) Evidence suggests that browser choice and grade level are independent.

c) There is not enough evidence to suggest that browser choice and grade level are independent.

d) Evidence suggests that browser choice and grade level are dependent.

Answer 1

ANSWER::

	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
							Total
	200*85/495=34.343	100*85/495=17.172	195*85/495=33.485				85
	200*100/495=40.404	100*100/495=20.202	195*100/495=39.394				100
	200*125/495=50.505	100*125/495=25.253	195*125/495=49.242				125
	200*185/495=74.747	100*185/495=37.374	195*185/495=72.879				185

	(fo-fe)^2/fe
	5.990	3.569	1.268
	0.004	4.752	2.240
	0.0051	0.0025	0.0117
	3.1123	8.0764	0.0617

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   29.093                          
                              
Level of Significance =   0.05                          
Number of Rows =   4                          
Number of Columns =   3                          
Degrees of Freedom=(#row - 1)(#column -1) = (4- 1 ) * ( 3- 1 ) =   6                          
                              
p-Value =   0.0001   [Excel function: =CHISQ.DIST.RT(χ²,df) ]                      
Decision:    p-value < α , Reject Ho                          

Option:: (d) is correct...........

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