(Question 1) One question on a survey asked whether people believe in hell 812 out of 1,137 respondents to this question answered either "Yes, definitely" or "Yes, probably."

a. Find the point estimate of the population proportion who believe in hell.

b. Find the standard error for this sample proportion. What does it show?

c. The sampling distribution of the sample proportion is approximately normal for such a large sample. Find the margin of error for this point estimate when the confidence level is 95%. What does it show?

(Question 2) When 1,136 subjects were asked, "Do you believe in heaven?," 930 replied with yes.

a. Find a point estimate of the proportion of people who believe in heaven.

b. Find the standard error for this point estimate. What does it show?

c. Find the margin of error using a 95% confidence level and interpret it.

(CONTEXT)

A. The point estimate is ___(Round to two decimal places needed.)

B. The standard error is ___ (Round to four decimal places as needed.)

(B.2) What does it show (By the options)?

A. It estimates how much the sample proportion from samples like this vary from sample to sample.

B. It estimates the precision of a point estimate for a given confidence level.

C. It estimates how accurate the standard deviation of any given sample from that population is likely to be compared to the true population standard deviation.

D. It estimates how accurate the mean of any given sample from that population is likely to be compared to the true population mean.

C. The margin of error is plus or minus

(C.2) Explain the meaning of the margin of error. Choose the correct answer below.

A. With 95% confidence, it can be stated that the population proportion is more than one margin of error lower or one margin of error higher than the reported sample proportion.

B. With 95% confidence, it can be stated that the population proportion is no more than one margin of error lower or one margin of error higher than the reported sample proportion.

C. With 95% confidence, it can be stated that the population proportion is more than half a margin of error lower or half a margin of error higher than the reported sample proportion.

D. With 95% confidence, it can be stated that the population proportion is no more than half a margin of error lower or half a margin of error higher than the reported sample proportion.