Question

The Manitoba Tourism Board plans to sample information centre visitors entering the province to learn the fraction of visitors who plan to camp in the province. Current estimates are that 30% of visitors are campers. How large a sample would you take to estimate at a 90% confidence level the population proportion with an allowable error of 7%? (Do not round the intermediate calculations. Round the final answer to the nearest whole number.)  

    

Sample size           

Answer 1

Solution =

Given,

E = 0.07

c = 90% = 0.90

or p = 30% = 0.30

1 - 1- p = 1 - 0.30 = 0.70

Now,

= 1 - c = 1 - 0.90 = 0.10

/2 = 0.05

= 1.645 (using z table)

The sample size for estimating the proportion is given by

n =

= (1.645)2 * 0.30 * 0.70 / (0.072)

= 115.9725

= 116 ..(round to the next whole number)

Answer : Required Sample size is n = 116