A new airline has just expanded its network to Australia and is interested in determining the proportion of its Australian customers who are flying overseas for business. Based on its experience in other markets, the airline estimates that the population proportion is 30%. It wants its confidence level to be 98%, and the error to be within 5%. How many random customers should the airline survey?
Question
A new airline has just expanded its network to Australia and is interested in determining the proportion of its Australian customers who are flying overseas for business. Based on its experience in other markets, the airline estimates that the population proportion is 30%. It wants its confidence level to be 98%, and the error to be within 5%. How many random customers should the airline survey?
Solution
To determine the sample size needed, we can use the formula for sample size in proportion:
n = (Z^2 * P * (1-P)) / E^2
where:
- n is the sample size
- Z is the Z-value from the standard normal distribution corresponding to the desired confidence level (for a confidence level of 98%, Z = 2.33)
- P is the estimated proportion of the population (in this case, 30% or 0.3)
- E is the desired margin of error (in this case, 5% or 0.05)
Substituting the given values into the formula, we get:
n = (2.33^2 * 0.3 * (1-0.3)) / 0.05^2
Solving this equation will give us the required sample size.
Similar Questions
A group of marketing students at a large university wants to determine the proportion of first year students who use certain types of social media. The students want their estimate to be within 0.03 of the true proportion with a 95% level of confidence. Two years ago, a similar study determined the proportion to be 0.796. How large of a sample is required?
Use the given data to construct a 99.5% confidence interval for the population proportion p.=x52, =n71Round the answer to at least three decimal places.Theconfidenceintervalis, .
An on-line retailing firm conducts a study into the number of on-line purchases of footwear made during all of last year. The study wants to determine the proportion of Australians over the age of 25 who purchase footwear on-line. The managing director of the on-line retailing firm believes this proportion of Australians is 22%. A random sample of 179 Australians over the age of 25 is selected. If the managing director’s claim is true, what is the sample proportion value below which 10% of all sample proportions would exist? Express your answer correct to two decimal places.
A marketing manager wants to conduct a survey to estimate the proportion of customers who are likely to repurchase a product. The manager wants a 90% confidence level. The population size of customers who have purchased the product in the past is estimated to be 2000. Using Slovin's formula, determine the required sample size for this survey.10 pointsYour answer
The CEO of a company wants to estimate the percent of employees that use company computers to go on Facebook during work hours with 95% confidence. He selects a random sample of 150 of the employees and finds that 53 of them logged onto Facebook that day. What is the estimate of the standard error of the proportion ?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.