A study was recently conducted at a major university to estimate the difference in the proportion of business school graduates who go on to graduate school within five years after graduation and the proportion of non-business school graduates who attend graduate school. A random sample of 400 business school graduates showed that 75 had gone to graduate school while in a random sample of 500 non-business graduates, 137 had gone on to graduate school. Based on a 95 percent confidence level, what is the upper limit of the confidence interval estimate? Round to three decimal places.

And the 95% confidence interval would be given (0.032;0.141).  

We are confident at 95% that the difference between the two proportions is between

The upper bound would be 0.141.

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".  

Solution to the problem

represent the real population proportion of business school graduates who go on to graduate school within five years after graduation

represent the estimated proportion of business school graduates who go on to graduate school within five years after graduation

is the sample size

represent the real population proportion of non-business school graduates who attend graduate school

represent the estimated proportion of non-business school graduates who attend graduate school

is the sample size required for Brand B

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 (0.032;0.141).  

We are confident at 95% that the difference between the two proportions is between

The upper bound would be 0.141.

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