Question

Sandy was interested in where her friends' responses to an event invitation(definite yes, definite no, maybe, no response) would differ depending on their primary method of travel (car or bus). The results are displayed in the following table. Using the .05 significance level, is the type of response independent of type of travel?

Definite Yes Definite No Maybe No response

car 10 3 9 8

bus 20 10 8 32

\Use the fives steps of hypothesis testing

Sketch the chi-square distribution. Be sure your sketch gives a rough indication of its shape and shows the cutoff score, sample score, and region of rejection

Answer 1

Answer

Step 1 -> Null hypothesis H0 : no association between mode of transport and response.
Alternative hypothesis H1 : association between the two variables.

step 2 -> Make the table.

	Definite yes	definite no	maybe	no reponse	Total
Car	10	3	9	8	30
train	20	10	8	32	70
Total	30	13	17	40	100

Step 3 : Calculate the expected frequencies ( =Row total * Column total/total)

	Definite yes	definite no	maybe	no reponse	Total
Car	9	3.9	5.1	12	30
train	21	9.1	11.9	28	70
Total	30	13	17	40	100

Step 4 : Calculate chi-square statistic.
Chi-square = $\sum$(observed - expected)²/expected = 6.620699

Step 5 : Critical value = Upper 95% point of chi-square distribution with df = (#rows-1)*(#columns-1) = 3
=7.814728
Since calculated chi-square < critical value, we accept H0 and conclude that there is no significant association between the two variables.

p-value =

0.08505

pdf f(x) v p= Pr[X > 1?]

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