Question

Please explain by what the below data means in regards to the test for independence. Thank you!

Observed frequencies

Likely Purchase	Chevy	Ford	Honda	Total
Yes	68	128	114	310
No	57	72	61	190
Total	125	200	175	500

Expected frequencies:

Likely Purchase	Chevy	Ford	Honda	Total
Yes	77.50	124.00	108.50	310.00
No	47.50	76.00	66.50	190.00
Total	125.00	200.00	175.00	500.00

p-value:

0.126327

Answer 1

In the first table above, we are given the observed frequencies O_i for each of the 6 cells. Using the row sums and columns sums in the first table, the expected values for each of the cells is computed as:

E_i = (Row Sum)*(Column Sum ) / Total Frequency

Where Total Frequency = 500

These expected frequencies are shown in the second table above.

Now using the observed and expected frequencies, the chi square test statistic is computed here as: ( Using test stat. )

Now degrees of freedom is computed as:

DF = (num of rows - 1)(num of columns - 1) = (2 - 1)(3 - 1) = 2

Using this the p-value is computed from the chi square distribution tables as:

This is what is displayed at the last above.