his Question: 1 pt 6 of 23 (2 complete) This Te In a survey of 3290 adults, 1418

Question

his Question: 1 pt 6 of 23 (2 complete) This Te In a survey of 3290 adults, 1418 say they have started paying bills online in the last year Construct a 99% confidence interval for the population proportion Interpret the result A 99% confidence interval for the population proportion is (Round to three decimal places as needed) Interpret your results. Choose the correct answer below olts of the gen fence interval A with 99% confidence itcan be said that the population proportion of aduts who say they have started paying bils o line in the last year is between the e B. The endpoints of the given confidence interval show that adults pay bills online 99% of the time oc. with 99% confidence, it can be said that the sample proportion of adults who say thy have started paying bas orne in the last year is between the e dpirts ofthe pon codden eme val

Explanation / Answer

Solution:

Here, we have to find out the 99% confidence interval for the population proportion.

Formula for confidence interval for population proportion is given as below:

Confidence interval = P -/+ Z*sqrt(P*(1 – P)/N)

Where, P is sample proportion, Z is critical value, and N is sample size.

WE are given

X = 1418

N = 3290

P = X/N = 1418/3290 = 0.43100304

Confidence level = 99%

Critical Z value = 2.5758

Confidence interval = P -/+ Z*sqrt(P*(1 – P)/N)

Confidence interval = 0.43100304 -/+ 2.5758*sqrt(0.43100304*(1 - 0.43100304)/3290)

Confidence interval = 0.43100304 -/+ 2.5758* 0.0086

Confidence interval = 0.43100304 -/+ 0.0222

Lower limit = 0.43100304 - 0.0222 = 0.4088

Upper limit = 0.43100304 + 0.0222 = 0.4532

Confidence interval = (0.409, 0.453)

A 99% confidence interval for the population proportion is (0.409, 0.453).

Correct alternative for interpretation:

A. With 99% confidence, it can be said that the population proportion of adults who say they have started paying bills online in the last year is between the endpoints of the given confidence interval.

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