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(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.

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Answer:

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.  

Step-by-step explanation:

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

[tex]H_{0}[/tex]: p=0.12

[tex]H_{a}[/tex]: p<0.12

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

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

  • p(s) is the sample proportion of trips included visit to a theme park ([tex]\frac{178}{1565}=0.1137[/tex]
  • p is the proportion assumed under null hypothesis. (0.12)
  • N is the sample size (1565)

Using the numbers, z=[tex]\frac{0.1137-0.12}{\sqrt{\frac{0.12*0.88}{1565}}}[/tex]

= −0.767 and p(z) is ≈0.222

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

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