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In: Statistics and Probability

In a survey of 4004 ​adults, 701 oppose allowing transgender students to use the bathrooms of...

In a survey of 4004 ​adults, 701 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.

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Expert Solution

Let p be the population proportion of appose allowing transgender students to use the bathrooms of the opposite biological sex.

n = number of adults in a survey = 4004.

X: Number of adults appose allowing transgender students to use the bathrooms of the opposite biological sex. = 701

phat : sample proportion

phat = X / n = 701 / 4004 =0.1751

Since the distribution of sampling proportion is normal.

We use normal distribution to find confidence interval for population proportion.

99% Confidence interval for population proportion is

Alpha: level of significance = 0.01

From normal probability table

Hence 99% confidence interval is

=(0.1751 -0.0155, 0.1751+ 0.0155)

=(0.1596, 0.1906).

Interpretation: The 99% true value of population proportion lies between 15.96% to 19.06%.

orchestra answered 2 years ago
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