John has 260 apples. 1/2 of the apples are green and 1/4 of the apples are bad. The rest of the apples are red. How many red app
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Answer:
And the 95% confidence interval would be given (-0.1412;-0.0318).
We are confident at 95% that the difference between the two proportions is between
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the real population proportion for business
represent the estimated proportion for Business
is the sample size required for Business
represent the real population proportion for non Business
represent the estimated proportion for non Business
is the sample size required for non Business
represent the critical value for the margin of error
The population proportion have the following distribution
Solution to the problem
The confidence interval for the difference of two proportions would be given by this formula
For the 95% confidence interval the value of and
, with that value we can find the quantile required for the interval in the normal standard distribution.
And replacing into the confidence interval formula we got:
And the 95% confidence interval would be given (-0.1412;-0.0318).
We are confident at 95% that the difference between the two proportions is between