In: Statistics and Probability
Problem Definition: People of differing ages turn to a variety of media to get their news. A study indicated the various age groups receive their news from the media groups shown in the following contingency table.
Medium |
Under 36 years of age |
36-50 years of age |
Above 50 years of age |
Local TV |
107 |
119 |
133 |
National TV |
73 |
102 |
127 |
Radio |
75 |
97 |
109 |
Local Newspaper |
52 |
79 |
107 |
Internet |
95 |
83 |
76 |
Set up your spreadsheet as shown below and do not enter row or column totals (do not include in report). Set alpha at .05
The hypothesis being tested is:
H0: The media source and age are independent
Ha: The media source and age are dependent
Medium | Under 36 years of age | 36-50 years of age | Above 50 years of age | Total | |
Local TV | Observed | 107 | 119 | 133 | 359 |
Expected | 100.64 | 120.17 | 138.19 | 359.00 | |
O - E | 6.36 | -1.17 | -5.19 | 0.00 | |
(O - E)² / E | 0.40 | 0.01 | 0.20 | 0.61 | |
National TV | Observed | 73 | 102 | 127 | 302 |
Expected | 84.66 | 101.09 | 116.25 | 302.00 | |
O - E | -11.66 | 0.91 | 10.75 | 0.00 | |
(O - E)² / E | 1.61 | 0.01 | 0.99 | 2.61 | |
Radio | Observed | 75 | 97 | 109 | 281 |
Expected | 78.77 | 94.06 | 108.17 | 281.00 | |
O - E | -3.77 | 2.94 | 0.83 | 0.00 | |
(O - E)² / E | 0.18 | 0.09 | 0.01 | 0.28 | |
Local Newspaper | Observed | 52 | 79 | 107 | 238 |
Expected | 66.72 | 79.67 | 91.62 | 238.00 | |
O - E | -14.72 | -0.67 | 15.38 | 0.00 | |
(O - E)² / E | 3.25 | 0.01 | 2.58 | 5.84 | |
Internet | Observed | 95 | 83 | 76 | 254 |
Expected | 71.21 | 85.02 | 97.77 | 254.00 | |
O - E | 23.79 | -2.02 | -21.77 | 0.00 | |
(O - E)² / E | 7.95 | 0.05 | 4.85 | 12.85 | |
Total | Observed | 402 | 480 | 552 | 1434 |
Expected | 402.00 | 480.00 | 552.00 | 1434.00 | |
O - E | 0.00 | 0.00 | 0.00 | 0.00 | |
(O - E)² / E | 13.39 | 0.17 | 8.63 | 22.18 | |
15.51 | critical value | ||||
22.18 | chi-square | ||||
8 | df | ||||
.0046 | p-value |
The p-value is 0.0046.
Since the p-value (0.0046) is less than the significance level (0.05), we can reject the null hypothesis.
Therefore, we can conclude that the media source and age are dependent.
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