How do I find relative sample statistic?

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 do I calculate my relative sample statistic and what is a relative sample statistic?

Answer 1

When you conducted your survey, you calculated a sample proportion of people who said they spent more than 4 hours on their phones daily.

p* = 0.95

n = 40

The claim is that 75% of the population spends omre than 4 hours on their phone daily.

p₀ = 0.75

The relative sample statistic for this scenario is given by the following:

z = [p* - p₀] / (standard error)

standard error =  √(p₀*(1-p₀)/n)

standard error =  √(0.75*(1-0.75)/40) = 0.068465

z = [0.95 - 0.75] / 0.068465 = 2.921