Question

Homework 8 ANOVA

An ad company was interest in determining the amount of money that should be spent in Nevada for the upcoming democratic primary. The theory is that more money should be spent on TV ads that reached more people. They decided to survey people to determine which news station they watched and then recommend to candidates where ads should be placed. They randomly sampled people that watched three news stations and found the following number of people, in thousands, from different major cities in Nevada watched these outlets as their primary way of obtaining news. (Russian bots hacked some of the cities, so the data was unreliable for some news outlet, hence there are unequal number of observations).

MSNBC	FOX	PBS
10	11	2
12	15	3
14	16	5
16	18	5
18		7
		8

1. What type of data are these values?
2. Can the results be generalized? To whom? Explain.
3. Test the null hypothesis that the mean number of people watching these stations are equal. Use an alpha of .10.
4. Calculate eta square and interpret.
5. Construct the three confidence intervals and write an interpretation of what they indicate

Answer 1

(a) This is a One-Way ANOVA test.

(b) The results can be generalized to people from all major cities in Nevada.

(c) The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃

H_a: Not all means are equal

Source	SS	df	MS	F	p-value	n²
Treatment	323.33	2	161.667	21.09	.0001	0.78
Error	92.00	12	7.667
Total	415.33	14

The p-value is 0.0001.

Since the p-value (0.0001) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that the mean number of people watching these stations are not equal.

(d) n² = 0.78

This is a large effect.

(e) Tukey Simultaneous Tests for Differences of Means

Difference of Levels	Difference of Means	SE of Difference	95% CI	T-Value	Adjusted P-Value
FOX - MSNBC	1.00	1.86	(-3.95, 5.95)	0.54	0.854
PBS - MSNBC	-9.00	1.68	(-13.47, -4.53)	-5.37	0.000
PBS - FOX	-10.00	1.79	(-14.76, -5.24)	-5.60	0.000

There is a significant difference between FOX and PBS.

There is a significant difference between PBS and MSNBC.