Question

Test at the 0.01 level the statement that 55% of those families who plan to purchase a vacation residence in Florida want a condominium. The null hypothesis is π=.55 and the alternative is π≠.55. A random sample of 300 families who planned to buy a vacation residence revealed that 218 families want a condominium. What decision should be made regarding the null hypothesis?

Answer 1

H0: = 0.55

Ha: 0.55

Sample proportion = 218 / 300 = 0.7267

Test statistics

z = ( - ) / sqrt [ ( 1 - ) / n ]

= ( 0.7267 - 0.55) / sqrt [ 0.55 ( 1 - 0.55) / 300 ]

= 6.15

This is test statistics value.

Critical values at 0.01 significance level = -2.576 , 2.576 (From Z table)

Since test statistics > 2.576 , Reject the null hypothesis