Make 4 claims (Goodness of fit claim for the categorical data (which web browser
ID: 3265982 • Letter: M
Question
Make 4 claims (Goodness of fit claim for the categorical data (which web browser do you use most often) claim for discrete data(social media column), claim for continuous data (how many minutes did you study yesterday and an Independence claim or Test of Homogeneity for the contingency table) These claims are in sentence form. Test each of your claims using a level of significance of.02 Using the p-value method. Show all steps. The test values can be found by the calculator if possible. The p-values must be found using Excel. State which formula you used. There is a total of 4 Hypothesis Tests (one for each claim)Explanation / Answer
Solution
Test 1: Goodness of Fit on Most-often used browser.
From the given data, following browser-wise frequency distribution is obtained. Let this frequency for ith browser be Oi.
Claim : All browsers are equally used.
Hypotheses: H0: All browsers are equally used.
Vs
Alternative: HA: H0 is false.
Test Statistic
2 = [i = 1 to 6]{(Oi - Ei)2/Ei}, where Ei = expected frequency for the ith browser , which under
H0 , = total frequency/total number of browsers. = 36/6 = 6 for all i's.
Calculations
Browser No i
1
2
3
4
5
6
Browser
FF
GC
Safari
IE
Opera
ME
Total
Oi
10
12
7
2
1
4
36
Ei
6
6
6
6
6
6
36
(Oi - Ei)^2/Ei
2.67
6
0.17
2.67
4.17
0.67
16.33
So, 2Cal = 16.33
Distribution and p-value
Under H0 , the above test statistic has Chi-square distribution with (n - 1) degrees of freedom, where n = number of browsers = 6.
So, p-value = P(25 > 16.33) = 0.0060 [using Excel Function]
Decision
Since p-value < level of significance (0.02) given, H0 is rejected.
Conclusion: There is sufficient evidence to suggest that the browsers have different usage frequency.
Done
Browser No i
1
2
3
4
5
6
Browser
FF
GC
Safari
IE
Opera
ME
Total
Oi
10
12
7
2
1
4
36
Ei
6
6
6
6
6
6
36
(Oi - Ei)^2/Ei
2.67
6
0.17
2.67
4.17
0.67
16.33
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