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.
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.
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(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.
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(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?
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