Question

In a recent survey, 2033 people were surveyed as to how many people preferred Tinder and how many people preferred Happn (a local dating website) and how many preferred Tinder in New York and Arizona. It was found that 1690/2033 people in New York liked using Tinder while 343/2033 preferred Happn and in Arizona, 1853/2033 people liked using Tinder while 180/2033 liked using Happn.

Construct and interpret a 95% confidence interval for the difference between the two dating website preferences.

***PLEASE DO NOT SOLVE THIS BY HAND AS I NEED TO COPY AND PASTE IT INTO A DISCUSSION. PLEASE TRY AND USE STAT CRUNCH IF POSSIBLE.***

Answer 1

We will find the 95% confidence interval for the difference between the two dating website preferences overall.

We need to construct the 95% 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 (X1​) =	1690+1853=3543
Sample Size 1 (N1​) =	2033+2033=4066
Favorable Cases 2 (X2​) =	343+180=523
Sample Size 2 (N2​) =	2033+2033=4066

The sample proportion 1 is computed as follows, based on the sample size N1​=4066 and the number of favorable cases X1​=3543:

The sample proportion 2 is computed as follows, based on the sample size N2​=4066 and the number of favorable cases X2​=523:

The critical value for α=0.05 is .

The corresponding confidence interval is computed as shown below:

Therefore, based on the data provided, the 95% confidence interval for the difference between the population proportions p1​−p2​ is 0.728<p<0.757, which indicates that we are 95% confident that the true difference between population proportions is contained by the interval (0.728,0.757).

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