Question

Presidential candidate Donald Trump caused quite a stir over his recent announcement to meet with the North Korean President. A sample of 400 hundred people were asked where they get their news and if they agree with the decision to meet with the North Korean President.

	Watches	Watches	Watches	Watches
	Fox News	CNN	MSNBC	Disney Channel
Should meet NKO Pres	60	50	60	55
Should not meet NKO Pres	30	70	20	55

a. At the 5% level does the above data support the hypothesis that ones opinions about the meetings and their favorite news channel are unrelated? Write out the expected frequency table.

Answer 1

We are given the data

Observed	Watches	Total
FOX	CNN	MSNBC	DISNEY
Should	60	50	60	55	225
Should not	30	70	20	55	175
Total	90	120	80	110	400

Null Hypothesis: Ones opinions about the meetings and their favorite news channel are unrelated

Alternate Hypothesis: Ones opinions about the meetings and their favorite news channel are related

Test Statistic:

Where are the Observed and expected values of the ijth Cell.  , are the ith Row and jth column totals with T being the overall Total.  

We shall now calculate the expected frequency table:

Expected	Watches	Total
FOX	CNN	MSNBC	DISNEY
Should	50.625	67.5	45	61.875	225
Should not	39.375	52.5	35	48.125	175
Total	90	120	80	110	400

O-E	Watches
FOX	CNN	MSNBC	DISNEY
Should	9.375	-17.5	15	-6.875
Should not	-9.375	17.5	-15	6.875

The Chi square critical value at 3 df=7.815 at 5% level of significance.

Since the calculated value 27.5131>tabulated value, we reject the Null hypothesis and conclude that at the 5% level the above data support that ones opinions about the meetings and their favorite news channel are related.

The expected frequency table:

Expected	Watches	Total
FOX	CNN	MSNBC	DISNEY
Should	50.625	67.5	45	61.875	225
Should not	39.375	52.5	35	48.125	175
Total	90	120	80	110	400