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 |
||
(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
Ha: 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.
Homework 8 ANOVA An ad company was interest in determining the amount of money that should...
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