Question

A travel agent claims that fewer than 12% of vacations include a trip to a theme park. A survey of 1680 people who took vacations recently revealed that 184 of them included a visit to a theme park. Test the travel agent's claim using the α=0.03 significance level.

(a) The test statistic is

(b) The P-value is

Answer 1

Solution:

Point estimate = sample proportion = = x / n = 0.110

This a left (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.12

Ha: p < 0.12

a)

Test statistics

z = ( - ) / *(1-) / n

= ( 0.110 - 0.12) / (0.12*0.88) /1680

= -1.26

b)

P-value = P(Z < z )

= P(Z < -1.26 )

= 0.1038