Question

In: Statistics and Probability

One of the questions on a survey of 1,000 adults asked if today's children will be...

One of the questions on a survey of 1,000 adults asked if today's children will be better off than their parents. Representative data are shown in the file 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? If required, round your answer to two decimal places.
_______
(b) At 95% confidence, what is the margin of error? If required, round your answer to four decimal places.
________
(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? If required, round your answers to four decimal places. Do not round your intermediate calculations.
_____ 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? If required, round your answers to four decimal places. Do not round your intermediate calculations.
______ to______
(e) Which of the confidence intervals in parts (c) and (d) has the smaller margin of error?

A. part (C) has the smaller margin of error

B. part (d) has the smaller margin of error
Why? (optional)
_______________________

Solutions

Expert Solution

Answer:

a)

Given,

sample proportion p^ = x/n

= 240/1000

= 0.24

Point estimate = 0.24

b)

Here at 95% CI, z value = 1.96

Consider,

Margin of error = z*sqrt(p^(1-p^)/n)

substitute values

= 1.96*sqrt(0.24(1-0.24)/1000)

= 0.0265

c)

Here at 95% CI, z value = 1.96

Consider,

Interval = p^ +/- z*sqrt(p^(1-p^)/n)

substitute values

= 0.24 +/- 1.96*sqrt(0.24(1-0.24)/1000)

= 0.24 +/-  0.0265

= (0.2135 , 0.2665)

d)

p^ = 530/1000 = 0.53

Here at 95% CI, z value = 1.96

Consider,

Interval = p^ +/- z*sqrt(p^(1-p^)/n)

substitute values

= 0.53 +/- 1.96*sqrt(0.53(1-0.53)/1000)

= 0.53 +/- 0.0309

= (0.4991 , 0.5609)

e)

Here we observe , the margin of error for part (C) is smaller than part(D).

orchestra answered 1 year ago
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