Question

Practice problems 1 – Type of variables
1. In the following situations give an example of a parameter and a statistic

a. Political elections
b. Subaru 2020 Forester vehicles c. RUM students
d. Puerto Ricans

2. You are in charge of a local company who wants to obtain mean income of the company’s engineers to compare with the mean income of engineers in the industry. You can either obtain the population mean (parameter) or a sample mean (statistic) to reach a managerial conclusion (both describing the same property, and assume both are feasibly possible to get). Which one would you rather use? Explain

3. Determine the type of variable in the following problems (Nominal, ordinal, quantitative). If quantitative state if it is discrete or continuous

a. Times power outages occur in Mayaguez Terrace last December b. Level of attraction of a person (de feo(a) a guapísimo(a))
c. Volume of chocolate by 25 kids sampled in October.
d. Sustained winds of hurricane Irene in the last 24 hours.

e. Placing at a marathon
f. Cell phone ownership (Yes, No) by citizens who are 50 or older

5. Of the examples above mention one that describes a parameter and one that describes a statistic.

Answer 1

1)a. In a political election, a parameter can be the number of influence a candidate has on the people. To measure this, a statistic : the total number of votes for that candidate can be appropriate.

Define Xi=1 if ith person votes for the candidate amd Xi=0 if ith person doesn't vote for the candidate. So summation Xi =total number of votes for the candidate is the statistic here.

B. Subaru 2020 Forester vehicles,

Parameter can be mileage of the car, statistic is the mean distance covered using 1 gallon of fuel.

C. Rum students, parameter is performance of the class in maths final exam whereas statistic is the average marks of the class in maths mid term exam.

2. If both the mean incomes are feasibly possible to get, one should go for the population mean income of the company as it includes engineers from different posts which may reflect difference in income. Also, a population enumeration is always better if possible as it gives accurate result in analysis than a sample.

3) a. Times power outages occur in Mayaguez Terrace last December : quantitative (discrete) as how many times can be counted.

b.Level of attraction of a person : ordinal (levels although qualitative can be ordered as very much, not so much etc)

C. Volume of chocolate by 25 kids sampled in October : quantitative (continuous)

D. Sustained winds of hurricane Irene in the last 24 hours : quantitative (discrete)

E. Placing at a marathon : ordinal

F. Cell phone ownership (Yes, No) by citizens who are 50 or older : nominal (no order is there in yes or no)

5.Cell phone ownership (Yes, No) by citizens who are 50 or older : is an example of parameter (if the study is on if older persons use cell phones or not and here entires population of >50 years is taken)

Times power outages occur in Mayaguez Terrace last December : statistic ( if we want to study the total power outage in the winter season, decmber month acts as a sample)