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In: Statistics and Probability

In a recent survey of 200 Instagram users, it was found that 71% of them were...

In a recent survey of 200 Instagram users, it was found that 71% of them were under the age of 35. Create and interpret a 95% Confidence Interval for the percentage of Instagram under the age of 35 using PANIC.

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Expert Solution

Solution :

Given that,

n =200

Point estimate = sample proportion = = 0.71

1 -   = 1- 0.71 =0.29

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

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

= 1.96 (((0.71*0.29) /200 )

= 0.0629

A 95% confidence interval for population proportion p is ,

- E < p < + E

0.71-0.0629 < p <0.71+ 0.0629

0.6471< p < 0.7729

The 95% confidence interval for the population proportion p is : 0.6471, 0.7729

orchestra answered 2 years ago
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