Question

A research firm regularly conducts customer satisfaction surveys for an amusement park. A survey of 100 randomly selected park visitors on a weekday in May concluded the average age of visitors to the park was 37 years. When the survey was repeated with 100 randomly selected park visitors on a Saturday in May the average age of visitors to the park was determined to be 17 years

a) What is the population of interest in this situation?
b) How many samples were described?
c) Is the average age of 37 years a parameter or a statistic?
d) Tell whether this information represents a quantitative or qualitative variable? - age of the visitor - whether the visitor has a season pass
e) What possible explanation is there for the large difference in age between the two samples?

Answer 1

(a) The population of interest in this situation is the average age of visitors to the park in MAY during weekdays or weekends.

(b) Two samples are described in the above situation, that is;

• A survey of 100 randomly selected park visitors on a weekday in May.
• A survey of 100 randomly selected park visitors on a Saturday in May.

(c) The average age of 37 years is a statistic.

(d) The above information represents a quantitative variable.

(e) The possible explanation for the large difference in age between the two samples would be that during weekdays most of the teenagers or children below 20 years of age are not able to come to parks because of their schools, coachings or some studies related work.

Explanation:

We are given that a research firm regularly conducts customer satisfaction surveys for an amusement park. A survey of 100 randomly selected park visitors on a weekday in May concluded the average age of visitors to the park was 37 years.

When the survey was repeated with 100 randomly selected park visitors on a Saturday in May the average age of visitors to the park was determined to be 17 years.

(a) The population of interest in this situation is the average age of visitors to the park in MAY during weekdays or weekends.

(b) Two samples are described in the above situation, that is;

• A survey of 100 randomly selected park visitors on a weekday in May.
• A survey of 100 randomly selected park visitors on a Saturday in May.

(c) The average age of 37 years is a statistic as it is the sample average age of visitors to the park on a weekday, i.e.
`\bar X_1` = 37 years.

(d) The above information represents a quantitative variable because in this we are concerned about the average age of visitors in the park which is a numeric value and we are not interested in any qualitative aspect.

(e) The possible explanation for the large difference in age between the two samples would be that during weekdays most of the teenagers or children below 20 years of age are not able to come to parks because of their schools, coachings or some studies related work.

But during weekends like Saturday, the schools or coaching institutions are generally closed due to which they are able to come to parks to play and because of this there are large number of children below 20 years of age who visit parks on weekends.