How do I construct a confidence interval?

Question

In a survey I conducted of 40 U.S. adults (age 18 and over), 95% of them said they spent more than 4 hours on their phones daily. My claim for this study is "I believe more than 75% of individuals spend more than 4 hours on their phones a day." and I will be testing my claim with a significance level of 5%

My survey is testing for proportions.

How would I construct a confidence interval for my claim? Based on my confidence interval, how do I know if the data supports my claim?

Answer 1

You don't construct a confidence interval for your claim, you construct a rejection region for the null hypothesis.

The null hypothesis is that p = .75, and the alternative hypothesis is that p >= .75 (more than is stated). Thus, this is a 1-sided test.

In Excel, if you use = BINOM.INV(40,0.75,0.95), you get 34. Thus, we reject the null hypothesis that p = .75 in favor of your claim if >= 35 spend more than 4 hours on the phone. In this experiment, 90% of 40 or 36 spent more than 4 hours. As 36 >= 35, you reject the null hypothesis that p = .75 in favor of your claim.

By the way, note that =BINOM.DIST(33,40,0.75,1) gives a value of 0.903775406518895, and =BINOM.DIST(34,40,0.75,1) gives a value of 0.956726017427984. This is why 34 is the cutoff - it is the first value that the probability reaches .95.