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Chapter 8: Q 35. (page 522)

Selling online According to a recent Pew Research Center report, many

American adults have made money by selling something online. In a random sample of 4579American adults, 914reported that they earned money by selling something online in the previous year. Assume the conditions for inference are met.

Determine the critical value z* for a 98% confidence interval for a proportion.

b. Construct a 98% confidence interval for the proportion of all American adults who

would report having earned money by selling something online in the previous year.

c. Interpret the interval from part (b).

Short Answer

Expert verified

a. The critical value for 98%confidence interval is 2.33

b. The confidence interval for proportion is 0.1859<p<0.2133

c. The confidence interval lie between0.1859and0.2133

Step by step solution

01

Given Information

It is given that x=914

n=4579

Confidence Level =0.98

Level of significance=0.02

02

Critical Value

Using EXCEL FORMULA=ABS(NORMSINV(0.02/2)), critical valueZC=2.33

03

To construct 98% confidence interval for a proportion

Sample Proportion p^=xn

p^=9144579=0.1996

Margin of Error E=Z伪/2脳p^(1-p^)n

E=2.33脳0.1996(1-0.1996)4579

E=0.0137

Confidence Interval is (p^-E,p^+E)

(0.1996-0.0137,0.1996+0.0137)=(0.1859,0.2133)

98%confidence interval is0.1859<p<0.2133

04

Interpreting Confidence Interval

Based for given data and above calculations, there is 98%confidence that correct population proportion of American adults reported to earn money by selling online previous year lie between0.1859and0.2133.

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Most popular questions from this chapter

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