Question

(1 point) A survey of 1780 people who took trips revealed that 117 of them included a visit to a theme park. Based on those survery results, a management consultant claims that less than 88 % of trips include a theme park visit. Test this claim using the α=0.01 significance level.
The test statistic is  
The critical value is  

The conclusion is  
A. There is not sufficient evidence to support the claim that less than 8 % of trips include a theme park visit.
B. There is sufficient evidence to support the claim that less than 8 % of trips include a theme park visit.

Answer 1

Solution:- Given that n = 1780, X = 117

sample proportion p = 117 / 1780 = 0.0657

hypothesis:
H0: true P = 0.08 (null hypothesis)
Ha: true P < 0.08 (alternative hypothesis)

(test statistic) sigma s = sqrt(P*(1-P)/n) = sqrt(0.0657*(1-0.0657)/1780) = 0.0059

test statistic = (p^-P)/s = (0.0657 - 0.08)/0.0059 = -2.4237

P(Z < -2.4237) = 0.0077

critical value = -2.33

rejection region: test statistic > critical value

=> option B.There is sufficient evidence to support the claim that less than 8 % of trips include a theme park visit.

=> we reject hypothesis

option B, there is not sufficient evidence!