Answer:
Assuming a confidence level of 95%.
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.
The standard error for this case is given by:
And the 95% confidence interval for the difference of the two proportions would be given (0.115;0.719).
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 brand A
represent the estimated proportion for male
is the sample size required for male
represent the real population proportion for female
represent the estimated proportion for female
is the sample size required for female
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
Assuming a confidence level of 95%.
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.
The standard error for this case is given by:
And replacing into the confidence interval formula we got:
And the 95% confidence interval for the difference of the two proportions would be given (0.115;0.719).