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nickersia
 2 years ago
A large supermarket chain commissioned a survey to find out whether people favoured extended opening hours at the weekend. Four hundred people were surveyed in Cork and 88% said that they were in favour of extended opening hours.
At the 95% confidence level,
1. Calculate the margin of error
2. Calculate the confidence interval.
Any one help/tips? :)
nickersia
 2 years ago
A large supermarket chain commissioned a survey to find out whether people favoured extended opening hours at the weekend. Four hundred people were surveyed in Cork and 88% said that they were in favour of extended opening hours. At the 95% confidence level, 1. Calculate the margin of error 2. Calculate the confidence interval. Any one help/tips? :)

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kropot72
 2 years ago
Best ResponseYou've already chosen the best response.1Using the binomial distribution, the sample mean for the numbers supporting extending the opening hours is \[np=400\times 0.88\] and the sample standard deviation is given by \[\sigma=\sqrt{np(1p)}=\sqrt{400\times 0.88\times 0.12}\] The margin of error at the 95% confidence level is found by multiplying the sample standard deviation by 1.960

nickersia
 2 years ago
Best ResponseYou've already chosen the best response.0Why 1.960? Is it always like that?

kropot72
 2 years ago
Best ResponseYou've already chosen the best response.11.960 applies to a 95% degree of confidence. Other values are possible if other degrees of confidence are required. These are found from inverse Normal techniques. For example 2.576 applies to 99% confidence.
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