Question

A survey of 19401940 people who took trips revealed that 212212 of them included a visit to a theme park. Based on thosesurvery results, a management consultant claims that less than 1212 % of trips include a theme park visit. Test this claim using the α=0.01α=0.01 significance level.

The test statistic is _________?
The critical value is_______?

Answer 1

Solution :

The null and alternative hypothesis is

H₀ : p = 0.12

H_a : p < 0.12

n = 1940

x = 212

= x / n = 212 / 1940 = 0.1093

P₀ = 0.12

1 - P₀ = 1 - 0.12 = 0.88

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.1093 - 0.12 / [(0.12 * 0.88) / 1940]

= -1.453

Test statistic = -1.453

= 0.01

Z_0.01 = 2.326

Critical value = 2.326