FRQ 1

Amusement parks sell day passes and season passes. A day pass to Fun World costs $41 and provides admittance to the amusement park for one day. A season pass to Fun World costs $100 and provides unlimited admittance to the amusement park all season.

The manager of Fun World would likely be able to understand how frequently patrons visit the park. At the end of the season he selects two separate random samples: one of 30 patrons that did not buy a season pass and one of 30 patrons that did buy a season pass. The parallel boxplots show the distribution of number of visits per patron for the most recent season for these two samples.

A) Write a few sentences comparing the distributions of number of visits for the sample of patrons that did and did not buy a season pass.

B) The mean number of visits per patron among those that did not buy a season pass is 1.7 visits per patron. The mean number of visits per patron among those that did buy a season pass is 2.967 visits per patron. Are these values parameters or statistics? Explain.

C) The number of visits for the 30 patrons that bought season passes are:

1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 7 9 10

What proportion of these patrons would have paid less if they bought day passes rather than a season pass? Explain.

a) The number of visits between the patrons who buys the season passes shows higher frequency than those who did not buy season passes, in general. However, the minimum value of 1 visit is present for both cases.

b) The mean visits of the patrons are just PARAMETERS. If you want to test your hypothesis using hypothesis testing, the statistics are the z or t scores comparing the parameters (means).

c) The proportion who would have paid less are those with 2 or fewer visits because they would only just paid $82 instead of $100.

Number of patrons with 2 or fewer visits: 16

Total number of patrons who bought season passes: 30

Proportion who would've paid less = 16/30 = 0.5333

Step-by-step explanation:

I just did it

fichoh fichoh · Answer 2 · 2021-09-19T16:20:51+02:00

Boxplots gives diagrammatic representation of a distribution using box and whiskers.

Statistical values derived form a sample are called statistic while those obtained from population are called parameter.

The proportion of patrons who would have paid less is 0.533

We can briefly describe the distribution represented by the boxplot thus :

Minimum visit for those who purchased season ticket and those who didn't is the same with a value of 1.
Maximum visit for those who purchased season ticket is 7 ; while the maximum visit for those who didn't is 3
Both distributions have two outlier values each.

B.)

The mean values for the number of visits per patron are statistic. This is because the mean values are derived from a sample.

Statistical values derived from the population are called parameters.

C.)

Day pass = $41

Season pass = $100

In other to pay less by purchasing a day pass :

Number of visits must be ≤ 2

This means total amount paid = $(41 × 2) = $82

Number of patrons who had ≤ 2 visits = 16

Total Number of patrons = 30

Proportion who would have paid less :

Number of patrons who had ≤ 2 visits ÷ Total Number of patrons
16 ÷ 30 = 0.533

Therefore, the proportion of patrons who would have paid less is 0.533.

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