7. the owners of a wildlife park are considering an increase in entrance for adults (a) In a random sample of 100 adults, 56 said that they would pay the increased charge to visit the park. (i)...

7.

the owners of a wildlife park are considering an increase in entrance for adults

(a)
In a random sample of 100 adults, 56 said that they would pay the increased charge to visit the park.

(i) Calculate a 90% confidence interval for the proportion of all adults who would pay the increased charge.

(ii) If a 95% confidence interval was calculated, would it be narrower or wider than the 90% confidence interval? Explain your answer.

(b) Time spent in the park by family groups with children averages 135 minutes with a standard deviation of 15 minutes. The managers of the site add a play park and find that the average time spent in the park by a random sample of 25 family groups containing at least one child is 157.5 minutes.

1. 
   

   (i)  Carry out an hypothesis test at the 5% significance level to see whether the mean time spent in the park is now greater than 135 minutes.

   
   


2. 
   

   (ii)  Calculate a 95% confidence interval for the mean time spent in the wildlife park after the play park is added. What can you conclude about the mean increase in time as a result of the addition of the play park?