Question

In Exercises 1–6, refer to the data below, which are total home game playing times (hours) for all Major League Baseball teams in a recent year (based on data from Baseball Prospectus).

236 237 238 239 241 241 242 245 245 245 246 247 247 248 248 249 250 250 250 251 252 252 253 253 258 258 258 260 262 264

Data Type

a. The listed playing times are all rounded to the nearest whole number. Before rounding, are the exact playing times discrete data or continuous data?

b. For the listed times, are the data categorical or quantitative?

c. Identify the level of measurement of the listed times: nominal, ordinal, interval, or ratio.

d. Which of the following best describes the sample data: voluntary response sample, random sample, convenience sample, simple sample?

e. The listed total game times are from one recent year, and the data are available for all years back to 1950. Given that the listed times are part of a larger collection of times, do the data constitute a sample or a population?

Short answer

a.The playing times are a type of continuous data.

b.The data is quantitative.

c.The playing times are measured on a ratio scale.

d. The sample of playing times is a convenience sample.

e. The data given is a sample.

Step-by-step solution

Given information

Data are given on the number of hours played in Major League Baseball by a set of teams.

Describe whether the data type is continuous or discrete 

a.

Data that can be measured can fall in an interval and can take any value (including decimals) is called continuous data.

Data that cannot be measured and has a fixed value is called discrete data.

As the number of hours can take up decimal values and are not fixed, the given data is continuous.

Describe whether the data type is quantitative or categorical 

b.

Data that consists of numbers are called numerical data, and data that includes names/labels are called categorical data.

As playing hours have numbers and not labels, the given data is quantitative.

Describe the measurement of scale 

c.

When the data has a well-defined natural zero value, and the ratio of the values ismeaningful, the data is measured on a ratio scale.

Here, the value of 0 hours means the game has just started and has not completed an hour and the playing time equal to 2 hours is twice as long as the playing time equal to 1 hour.

Therefore, the playing times are measured on a ratio scale.

Describe the type of sampling method

d.

As the number of playing hours was recorded for the set of readily available teams to the researcher, the sampling method used is convenience sampling.

Therefore, the given data is a convenience sample.

Describe whether the data type is sample or population

e.

The set of all the observations of a variable is called the population.

A small set of observations selected from the population is called a sample.

Here, the playing times are given for one year when the values are available for a large number of years.

Thus, it can be said that the given data is a sample and not the population.