Question

In: Statistics and Probability

The success of the Facebook business model depends on users clicking on ads when using the...

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)

Expert Solution

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 * $\sqrt$ (( * (1 - )) / n)

= 1.645 * $\sqrt$ ((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

orchestra answered 2 years ago

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