Question

For the following problem, do not round until the end. Round all

final answers to the nearest whole number percent.
In a large population, 61% of people support prop A. A sample of
100 adults is taken. What proportion do we expect will support
prop A? What standard error do we expect? Fill in the following
blanks:
• In 68% of samples, between
I
% and
% of people will support prop A.
• In
% of samples, between 51% and 71%
of people will support prop A.
• In 99.7% of sample, between
% and
% of people will support prop A."

Answer 1

To find the proportion of people supporting prop A in the sample, multiply the sample size by the percentage of people supporting prop A. Divide the number of people supporting prop A by the sample size to find the proportion. To determine the standard error, use the formula √[(p * (1 - p)) / n], where p is the proportion and n is the sample size.

Step-by-step explanation:

To find the proportion of people who support prop A in the given sample, we first determine the number of people who support prop A. Since the sample size is 100 and 61% of people support prop A, we can calculate the number of people by multiplying 100 and 0.61.

We expect approximately 61 people to support prop A in the sample. To find the proportion, we divide the number of people who support prop A by the sample size, giving us 61/100.

Thus, the proportion of people we expect to support prop A is 0.61. To find the standard error, we can use the formula √[(p * (1 - p)) / n], where p represents the proportion and n represents the sample size. Plugging in the values, we get √[(0.61 * (1 - 0.61)) / 100].

Calculating this, we find the standard error is approximately 0.048, which we can round to 0.05.