Question

(3) A computer-gaming entrepreneur who develops and sells new games to major manufacturers of systems such as Xbox™, Wii™, and PS3™ wants to estimate the percentage of households with teenagers, that own any of these gaming systems. The entrepreneur randomly selects 500 households with teenagers and performs a survey to determine whether or not each household owns an Xbox™, Wii™, PS3™, or some similar system. He determines that 421 of the households he surveyed own such systems.

(a) Determine the criteria for approximate normality.

(b) What is the sample proportion?

(c) What is standard error for the sampling distribution?

(d) Compute the margin of error.

(e) Determine the 95% confidence interval for population proportion.

(f) Interpret the 95% confidence interval in context.

Answer 1

a) here as sample is random ; np(1-p)>=10 ; therefore the distribution is approximate normal.

b)

sample proportion =0.842

c) standard error for the sampling distribution =0.0163

d) margin of error =0.0319

e)

95% confidence interval for population proportion =0.8101 <p<0.8739

f) above interval gives 95% confidence to contain true population proportion of the households who   own such systems. ( Xbox™, Wii™, PS3™ )