When 355 college students are randomly selected and surveyed, it is found that 129 own a...

When 355 college students are randomly selected and surveyed, it is found that 129 own a car. Construct a 96% confidence interval for the percentage of all college students who own a car. (3 decimal places)

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Expert Solution

Solution :

n = 355

x = 129

= x / n = 129 / 355 = 0.363

1 - = 1 - 0.363 =0.637

At 96% confidence level the z is ,

= 1 - 96% = 1 - 0.96 = 0.04

/ 2 = 0.04 / 2 = 0.02

Z_/2 = Z_0.02 = 2.054

Margin of error = E = Z_{/ 2} * $\sqrt$ (( * (1 - )) / n)

= 2.054 * ( $\sqrt$ ((0.363 * 0.637) / 355)

= 0.052

A 96 % confidence interval for population proportion p is ,

- E < P < + E

0.363 - 0.052 < p < 0.363 + 0.052

0.311 < p < 0.415

21.1% < P < 41.5%

orchestra answered 1 year ago

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