Question

We are interested in developing a mobile phone application for two universities, Middle America State University (MASU) and Small Town Tech University (STTU). However, we are unsure if there is a difference in the type of phones used at the two universities, and need to consider the distribution of Android users vs. iPhone users at the two universities to decide whether to develop the app for iOS or Android . To help her make our decision, we take a random sample of 75 students from MASU and 80 students from STTU. All students used either an iPhone or an Android, and found that 42 used an Android in the sample from MASU compared to 48 at STTU.

To help make our decision, create a 90% confidence interval for the difference in the proportion of students that use an Android phone at each university.

Show your work as best you are able below; try to label all variables as clearly as possible.

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Answer 1

We need to construct the 90% confidence interval for the difference between population proportions p1​−p2​.

We have been provided with the following information about the sample proportions:

Favorable Cases 1 (MASU​) =	42
Sample Size 1 (MASU) =	75
Favorable Cases 2 (STTU​) =	48
Sample Size 2 (STTU​) =	80

The sample proportion MASU is computed as follows,

based on the sample size N_1 = 75

and the number of favorable cases X_1 = 42:

The sample proportion 2 is computed as follows,

based on the sample size N2​=80

and the number of favorable cases X_2 = 48

The critical value for α=0.1 is

The corresponding confidence interval is computed as shown below:

Therefore, based on the data provided, the 90% confidence interval for the difference between the population proportions p1​−p2​ is −0.17<p<0.09,

which indicates that we are 90% confident that the true difference between population proportions is contained by the interval (-0.17, 0.09).

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