In: Statistics and Probability
What effect does noise pollution have? Mathews and Canon (1975) had a person with a cast on one arm get out of a car and drop an armload of books in front of pedestrians. Will the pedestrians help? Sometimes there was a loud gasoline lawn mower operating (Noise) nearby when the books were dropped and sometimes the mower was not operating (No Noise). Of the 25 pedestrians who were in the Noise condition, 4 helped. Of the 25 pedestrians who were in the No Noise condition, 20 helped. Analyze the numbers and write an explanation of the effects of noise pollution. Please show how you allocated the frequency before calculating. Please show all work for credit. Also show the critical value.
Answer:
Noise
No Noise
Helped
Did not help
The hypothesis being tested is:
H0: There is no effect of noise pollution
Ha: There is an effect of noise pollution
Noise | No Noise | Total | ||
Helped | Observed | 4 | 20 | 24 |
Expected | 12.00 | 12.00 | 24.00 | |
O - E | -8.00 | 8.00 | 0.00 | |
(O - E)² / E | 5.33 | 5.33 | 10.67 | |
Did not help | Observed | 21 | 5 | 26 |
Expected | 13.00 | 13.00 | 26.00 | |
O - E | 8.00 | -8.00 | 0.00 | |
(O - E)² / E | 4.92 | 4.92 | 9.85 | |
Total | Observed | 25 | 25 | 50 |
Expected | 25.00 | 25.00 | 50.00 | |
O - E | 0.00 | 0.00 | 0.00 | |
(O - E)² / E | 10.26 | 10.26 | 20.51 | |
3.841 | critical value | |||
20.51 | chi-square | |||
1 | df | |||
5.92E-06 | p-value |
The p-value is 0.0000.
Since the p-value (0.0000) is less than the significance level (0.05), we can reject the null hypothesis.
Therefore, we can conclude that there is an effect of noise pollution.
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