Question

A survey of 1057 parents who have a child under the age of 18 living at home asked about their opinions regarding violent video games. A report describing the results of the survey stated that 89 % of parents say that violence in today's video games is a problem. (a) What number of survey respondents reported that they thought that violence in today’s video games is a problem? You will need to round your answer. X = (b) Find a 95% confidence interval ( ±0.001) for the proportion of parents who think that violence in today's video games is a problem. 95% confidence interval is from to (c) Convert the estimate of your confidence interval to percents ( ±0.1) % to %

Answer 1

n = total number of parents in a survey = 1057

p = proportion of the parents who say that violence in today's video games is a problem = 0.89

(a) What number of survey respondents reported that they thought that violence in today’s video games is a problem?

X = n*p = 1057*0.89 = 940.73 = 941

Find a 95% confidence interval ( ±0.001) for the proportion of parents who think that violence in today's video games is a problem.

b) Formula of confidence interval for population proportion is

Where E is called margin of error

Formula of E is

......( 1 )

It is given that ; c = confidence level = 0.95

so that level of significance = = 1 - c = 1 - 0.95 = 0.05

this implies that \alpha/2 = 0.05/2 = 0.025

So we want to find Z_{/2} such that

P(Z >Z _/2) = 0.025

Therefore ,

P(Z < Z _/2) = 1 - 0.025 = 0.975

The general excel command to find critical z value is

"=NORMSDIST(probability)"

Here probability = 0.975

So that critical Z _/2 is = "=NORMSINV(0.975)" = 1.96

also n = 1057 and = 0.89

Put this value in equation (1) so we get

So E = 0.019

Lower limit = - E = 0.89 - 0.019 = 0.871

Upper Limit = + E = 0.89 + 0.019 = 0.909

So that 95% confidence interval for population proportion P is (0.871 , 0.909)

c)  Convert the estimate of your confidence interval to percents ( ±0.1) % to %

The confidence interval to percents ( ±0.1) 87.1% to 90.9%