A professional hockey researcher wants to determine the true proportion of people who think fighting should not be part of the game. After surveying 800 fans at a hockey game the survey found that 212 people think fighting should not be part of the game. Construct a 90% confidence interval for the true proportion.
Solution :
Given that,
Point estimate = sample proportion =
= x / n = 212 / 800 = 0.265
Z/2
= 1.645
Margin of error = E = Z
/ 2 *
((
* (1 -
)) / n)
= 1.645 * (((0.265
* 0.735) / 800)
= 0.026
A 90% confidence interval for population proportion p is ,
- E < p <
+ E
0.265 - 0.026 < p < 0.265 + 0.026
0.239 < p < 0.291
(0.239 , 0.291)
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