Question

6. Digital streaming has shifted some of the focus from traditional TV commercials to online advertisements.
The Harris poll reported in 2012 that 53% of 2,343 American adults surveyed said they watched digitally
streamed content. Calculate and interpret a 99% score CI for the proportion of all adult Americans
who watched digitally streamed content.

Answer 1

6)

Solution :

Given that,

n = 2343

Point estimate = sample proportion = = 53% = 0.53

1 - = 1 - 0.53 = 0.47

At 99% confidence level the z is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 2.576 * (((0.53 * 0.47) / 2343)

= 0.027

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.53 - 0.027 < p < 0.53 + 0.027

0.503 < p < 0.557

The 95% confidence interval for the population proportion p is : (0.503 , 0.557)