Question

According to research conducted by the fictional agency entitled Birth Rate and Health Outcomes, a sample of 3,000 women who gave birth reported that the mean age of first-time mothers in the U.S. was 24.5 years old with a median age of 24 and a standard deviation of 2.91.

a. What is the point estimate of the population mean?

b. Based on the limited information presented, is this distribution likely to be skewed right, left, or normal? Explain.

c. Compute the 95% confidence interval of the population mean and interpret it.

d. Is it plausible that the population mean could be equal to 24? Explain.

Answer 1

a. Here it is given that for a sample of 3,000 women who gave birth reported that mean age of first-time mothers in the U.S. was 24.5 years old.

As n is sufficient large as per central limit theorem, distribution is normal so point estimate of population mean is sample mean and its value is 24.5

b. As we know for right skewed distribution mean is greater than median and that is case here.

So answer is right skewed.

c. Now we need to find 95% CI

z value for 95% CI is 1.96 as

And also standard deviation is 2.91

So Margin of Error is

So Confidence interval is

d. As 24 is not in the range of confidence interval, It is not plausible that the population mean could be equal to 24