Question

(3 points) A survey of 15651565 people who took trips revealed that 178178 of them included a visit to a theme park. Based on those survery results, a management consultant claims that less than 1212 % of trips include a theme park visit. Test this claim using the α=0.05α=0.05 significance level.

Answer 1

We fail to reject the null hypothesis at 0.05 significance level. We cannot say that less than 12% of trips include a theme park visit.

Explanation:

let p be the proportion of trips included a visit to a theme park.

`H_(0)`: p=0.12

`H_(a)`: p<0.12

To test, we need to calculate test statistic of the sample proportion as:

z=
`\frac{p(s)-p}{\sqrt{(p*(1-p))/(N) } }` where

• p(s) is the sample proportion of trips included visit to a theme park (
  `(178)/(1565)=0.1137`

• p is the proportion assumed under null hypothesis. (0.12)

• N is the sample size (1565)

Using the numbers, z=
`\frac{0.1137-0.12}{\sqrt{(0.12*0.88)/(1565)}}`

= −0.767 and p(z) is ≈0.222

Since 0.222 > 0.05 we fail to reject the null hypothesis.