Question

Suppose that an alien lands on Earth, notices that there are two different sexes of the human species, and sets out to estimate the proportion of human beings who are female. Suppose that the alien chooses the members of the 1998 U.S. House of Representatives as its sample of human beings. In 1998, there were 53 representatives who were female and 382 representatives who were male. Create a 95% confidence interval for the population proportion of human beings who are female. Note: Your sample size is the total number of members in the 1998 US House of Representatives.

Option 1: 52.88 to 53.12
Option 2: 52.97 to 53.03
Option 3; 0.09 to 0.15
Option 4: 0.104 to 0.136

Answer 1

To create a 95% confidence interval for the proportion of human beings who are female, the sample proportion of female representatives is 53/435 = 0.12299. Using the formula and a Z-value of 1.96, we can calculate the error bound as 0.02956. The 95% confidence interval is therefore 0.09343 to 0.15255.

Step-by-step explanation:

To create a 95% confidence interval for the population proportion of human beings who are female, we can use the formula:

p' - EBP to p' + EBP

Where p' is the sample proportion and EBP is the error bound. In this case, the sample proportion is 53/435 = 0.12299 and the error bound can be calculated as:

EBP = Z * sqrt((p' * (1 - p')) / n)

Using a Z-value of 1.96 for a 95% confidence level and a sample size of 435 (total number of representatives), we can calculate EBP as:

EBP = 1.96 * sqrt((0.12299 * (1 - 0.12299)) / 435) = 0.02956

Substituting the values into the formula, we get:

0.12299 - 0.02956 to 0.12299 + 0.02956

which simplifies to:

0.09343 to 0.15255

Therefore, the 95% confidence interval for the proportion of human beings who are female is 0.09343 to 0.15255.