Past surveys reveal that 30% of tourists going to Las Vegas to gamble spend more

Question

Past surveys reveal that 30% of tourists going to Las Vegas to gamble spend more than $1,000. The Visitor’s Bureau of Las Vegas wants to update this percentage.

How many tourists should be randomly selected to estimate the population proportion with a 90% confidence level and a 1% margin of error. (Round your z value to 3 decimal places and final answer to the next whole number.)

The Bureau feels the sample size determined above is too large. What can be done to reduce the sample? Based on your suggestion, recalculate the sample size. (Hint: Use an allowable error in the range of 0.01 to 0.05.) (Round your z value to 3 decimal places and final answer to the next whole number.)

Explanation / Answer

Ans:

Prior estimate of p=0.3

Margin of error=0.01

z value for 90% confidence interval is 1.645

Sample size required,n=1.645^2*0.3*(1-0.3)/0.01^2=5683

Now,

Margin of error=0.05

Sample size required,n=1.645^2*0.3*(1-0.3)/0.05^2=228

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