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In: Statistics and Probability

In a survey of 3992 adults, 717 oppose allowing transgender students to use the bathrooms of...

In a survey of 3992 adults, 717 oppose allowing transgender students to use the bathrooms of the opposite biological sex. Construct a​ 99% confidence interval for the population proportion. Interpret the results.

A​ 99% confidence interval for the population proportion is (,)

Solutions

Expert Solution

Solution :

Given that,

n = 3992

x = 717

Point estimate = sample proportion = = x / n = 717/3992=0.180

1 - = 1 -0.180=0.820

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576 ( Using z table )

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

= 2.576 (((0.180*0.820) / 3992)

E = 0.0157

A 99% confidence interval for population proportion p is ,

- E < p < + E

0.180 -0.0157 < p <0.180+ 0.0157

0.1643< p < 0.1957

The 99% confidence interval for the population proportion p is : 0.1643, 0.1957

orchestra answered 2 years ago
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