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One of the questions on a survey of 1,000 adults asked if today's children will be better off than their parents (Rasmussen Reports website, October 26, 2012). Representative data are shown in the DATAfile named ChildOutlook. A response of Yes indicates that the adult surveyed did think today's children will be better off than their parents. A response of No indicates that the adult surveyed did not think today's children will be better off than their parents. A response of Not Sure was given by 23% of the adults surveyed.

a. What is the point estimate of the proportion of the population of adults who do think that today's children will be better off than their parents?

b. At 95% confidence, what is the margin of error (to 4 decimals)?

c. What is the 95% confidence interval for the proportion of adults who do think that today's children will be better off than their parents (to 3 decimals)? to

d. What is the 95% confidence interval for the proportion of adults who do not think that today's children will be better off than their parents (to 3 decimals)? to e. Which of the confidence intervals in parts (c) and (d) has the smaller margin of error?

Answer 1

Answe Date: 18/04/2019 a) The best estimate of population proportion of the population of adults who do think that today's children will be better off than their benefits is 240 1000 0.24 The best estimate of population proportionis0.24 b) At 95% confidence, the margin of error is. From the standard normal table, the z-critical value at 95 % confidence is 1 .96.

.10.24(1-024) 1000 =1.96 × 0.0265 At 95% confidence, the margin of error is l 0.0265- c) A 05s oasdenetarval for the popuiaion proportion of tl population of adults who do think that today's children will be better off than their benefits is, 95% CI, = p ± E 0.24 t0.0265 = 0.2135 to 0.2665 A 95% confidence interval for the population proportion of the population of adults who do think that today's children will be better off than their benefits is 0.2135 to 0.2665 d)

A 95% confidence interval for the population proportion the population ofadults who do not think that today's children will be better off than their benefits is, From the standard normal table, the z-critical value at 95 % confidence is 1 .96 p(l - p) 0.53 +196x53(-0.53) -0.530.0309 (Margin of Error) V1000 0.4991 to 0.5609 A 95% confidence interval for the population proportion the population of adults who do not think that today's children will be better off than their benefits is 0.4991 to 0.5609 e) The part (c) confidence interval has smaller margin of error due to the sample proportion in part (c) confidence interval is 0.24 smaller.