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.
1. a) Name the distribution used to construct CIs. (Show any conditions that you’ve checked.)
2. b) Find the 95% confidence interval for the population proportion of adults who enjoy video
  
  games.

Solutions

Expert Solution

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.

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 )

orchestra answered 1 year ago

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