Question

The success of the Facebook business model depends on users clicking on ads when using the web site. A random sample of 260 Facebook users found that 169 of them click on the ads. Determine the 90% confidence interval for this sample is given by , . (There is a unique answer to this question. Use the z-score from the table. Do not round your answers in the preceding steps. Round the final answers to three decimal places)

Answer 1

Solution :

Given that,

n = 260

x = 169

Point estimate = sample proportion = = x / n = 169/260=0.65

1 -   = 1- 0.65 =0.35

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.65*0.35) /260 )

= 0.049

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.65-0.049 < p <0.65+ 0.049

0.601< p < 0.699

The 90% confidence interval for the population proportion p is =0.601, 0.699