Question

A survey of 2281 adults in a certain large country aged 18 and older conducted by a reputable polling organization found that 419 have donated blood in the past two years. Complete parts (a) through (c) below. Click here to view the standard normal distribution table (page 1) Click here to view the standard normal distribution table (page 2) (a) Obtain a point estimate for the population proportion of adults in the country aged 18 and older who have donated blood in the past two years (Round to three decimal places as needed.) (b) Verify that the requirements for constructing a confidence interval about p are satisfied. The sample a simple random sample, the value of iswhich io10, and the less than or equal to 5% of the (Round to three decimal places as needed.) nhe ast wo ear c) Construct and interpret a 90% confidence interval for the population propor on o adults the country who have on correct choice below and fill in any answer boxes within your choice. Type integers or decimals rounded to three decimal places as needed. Use ascending order.) e ao Select e OA 0 There is a % chance the proportion of adults in the country aged 18 and older who have donated blood n the past two years s between and B. We are % confident the proportion of adults in the country aged 18 and older who have donated blood in the past two years is between and

Answer 1

The student's question involves computing a point estimate for the proportion of adults who have donated blood, verifying the requirements for constructing a confidence interval, and constructing and interpreting a 90% confidence interval for the true population proportion.

Step-by-step explanation:

The student's question relates to the construction of a confidence interval for the population proportion of adults in a country who have donated blood in the past two years, using survey data. To answer parts (a) through (c), we should start by calculating the point estimate for the population proportion, check the requirements for constructing a confidence interval, and finally construct and interpret the interval.

• (a) The point estimate for the proportion is found by dividing the number of adults who have donated blood by the total surveyed, which is 419/2281. Rounded to three decimal places, this gives us the point estimate.
• (b) To verify the requirements for constructing a confidence interval, we check if the sample is a simple random sample, that the sample size criteria are met (np > 10 and n(1-p) > 10), and the sample size is less than 5% of the population, where applicable.
• (c) The 90% confidence interval can be constructed using the formula for the margin of error around the point estimate and incorporating the standard normal distribution value (z-score) that corresponds to a 90% confidence level. The interpretation of this interval would specify the range within which the true population proportion is likely to be, with 90% confidence.

Factors such as sample bias and non-response can affect survey outcomes and are not covered by the margin of error. Decreasing the confidence level from 99% to 90% would result in a narrower confidence interval.