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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

10Bottling cola A particular type of diet cola advertises that each can contains 12 ounces of the beverage. Each hour, a supervisor selects cans at random, measures their contents, and computes a 95%confidence interval for the true mean volume. For one particular hour, the 95%confidence interval is 11.97ounces to 12.05ounces.

a. Does the confidence interval provide convincing evidence that the true mean volume is different than 12ounces? Explain your answer.

b. Does the confidence interval provide convincing evidence that the true mean volume is 12ounces? Explain your answer.

How confident? The figure shows the result of taking 25SRSs from a Normal population and constructing a confidence interval for the population mean using each sample. Which confidence level鈥攔ole="math" localid="1654197644211" 80%,90%,95%,or99%鈥攄o you think was used? Explain your reasoning.

Rating school food Latoya wants to estimate the proportion of the seniors

at her boarding school who like the cafeteria food. She interviews an SRS of 50of the 175 seniors and finds that 14 think the cafeteria food is good.

How confident? The figure shows the result of taking 25SRSs from a Normal population and constructing a confidence interval for the population mean using each sample. Which confidence level鈥�80%,90%,95%,or99%鈥攄o you think was used? Explain your reasoning.

Age and video games Refer to Exercise 41. The study also estimated that 67% of adults aged 18鈥�29play video games, but only 25%of adults aged 65and older play video games.

a. Explain why you do not have enough information to give confidence intervals for these two age groups separately.

b. Do you think a 95% confidence interval for adults aged 18鈥�29 would have a larger or smaller margin of error than the estimate from Exercise 41? Explain your answer.
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