A survey of 100 Americans found that 68% said they find it hard to buy holiday...

A survey of 100 Americans found that 68% said they find it hard to buy holiday gifts that convey their tr ue feelings. Find the 90% confidence interval of the population proportion.

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Expert Solution

Solution :

Given that,

n = 100

= 0.68

1 - = 1 - 0.68 = 0.32

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * ( $\sqrt$ ((0.68 * 0.32) / 100)

= 0.077

A 90% confidence interval for population proportion p is ,

- E < P < + E

0.680 - 0.077 < p < 0.680 + 0.077

0.603 < p < 0.757

(0.603 , 0.757)

orchestra answered 1 year ago

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