Question

1. A random sample of 400 families who planned to buy a vacation residence revealed that 250 families want to buy a condominium in Florida. The previous study shows that 55% of those families who plan to purchase a vacation residence in Florida want a condominium.

Required:

1. Can we conclude that there are more than 55% families who will buy the condominium in Florida, state your decision in terms of the null hypothesis. Use a 0.01 level of significance.                                                     
2. Calculate the p-value and briefly explain your answer.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p = 0.55

Ha : p > 0.55

n =400

x =250

= x / n = 250/400 = 0.62

P0 = 0.55

1 - P0 = 1 -0.55 =0.45

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.62-0.55 / [(0.55*0.45) / 400]

= 3.01

Test statistic = z =3.01

P(z > 3.01 ) = 1 - P(z < 3.01 ) = 1 -0.9987

P-value = 0.0013

= 0.01

P-value <

0.0013 < 0.01

Reject the null hypothesis .

There is sufficient evidence to suggest that