Question
In: Statistics and Probability
A gaming company is interested in the population proportion of adults who enjoy video games. They...
-
A gaming company is interested in the population proportion of adults who enjoy video games. They conduct a survey of 160 randomly selected adults and find that 48 enjoy video games.
-
a) Name the distribution used to construct CIs. (Show any conditions that you’ve checked.)
-
b) Find the 95% confidence interval for the population proportion of adults who enjoy video
games.
-
Solutions
Expert Solution
a)
Sample proportion 
= 48 / 160
= 0.3
n = 48 >=
10 , n(1- ) >=
10
The distribution of sample proportion is approximately normally distributed.
Distribution used to construct CI is normal distribution for proportion.
b)
95% confidence interval for proportion p is
-
Z
/2 * Sqrt [
( 1 -
) / n) <
p < +
Z/2 * Sqrt [
( 1 -
) / n)
0.3 - 1.96 * sqrt( 0.3 * 0.7 / 160) < p < 0.3 + 1.96 * sqrt( 0.3 * 0.7 / 160)
0.229 < p < 0.071
95% CI is ( 0.229 , 0.071 )
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