Use the information below to answer the questions. Online Service Usage You are

Question

Use the information below to answer the questions. Online Service Usage You are a travel agent and wish to estimate, with 98% confidence, the proportion of vacationers who use an online service or the internet to make travel reservations. Your estimate must be accurate to within 4% of the population proportion. Assume that no preliminary estimate is available. Find the minimum sample size needed. Find the minimum sample size needed, using a prior study that found that 30% of the respondents said they used an online service or the internet to make travel reservations. What do conclude about the effects of having a preliminary estimate from the results found in questions 23 and 24?

Explanation / Answer

23 ) if no estimate is available

n >= z^2 /(4*e^2)

z for 98 % level of confidence is 2.327

e = 0.04

hence

n >= (2.327/2/0.04)^2 = 846.0826

hence n = 847

24)if p^ =0.30

n >= z^2*pq /(e^2)

z for 98 % level of confidence is 2.327

e = 0.04

hence

n >= (2.327/0.04)^2 *0.3*0.7 = 710.70943

hence n = 711

25)if p^ is known ,then n (sample size required )decreases

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