Question

A manufacturer of jeans has plants in California, Arizona, and Texas. A group of 25 pairs of jeans is randomly selected from the computerized database, and the state in which each is produced is recorded.
CA AZ AZ TX CA
CA CA TX TX TX
AZ AZ CA AZ TX
CA AZ TX TX TX
CA AZ AZ CA CA

a. What is the experimental unit?
b. What is the variable being measured? Is it qualitative or quantitative?
c. Construct a pie chart to describe the data.
d. Construct a bar chart to describe the data.
e. What proportion of the jeans are made in Texas?
f. What state produced the most jeans in the group?
g. If you want to find out whether the three plants produced equal number of jeans, or whether one produced more jeans that the others, how can you use the charts from parts c and d to help you? What conclusions can you draw from these data?

Answer 1

Answer and Step-by-step explanation:

a) In statistics, an experimental unit is one member of a set of entities being studied. Experimental units are the individuals on whom an experiment is being performed on.

25 pairs of jeans are randomly selected, hence, a single experimental unit is a pair of jeans.

b) Variables are the qualities/topics being investigated. Qualitative variables puts the variables in categories while quantitative variables involve numerical variables.

This question focuses on which state each pair of jeans is being produced, therefore this quality categorizes the jeans according to which state they were produced in. Hence, the variable being measured is a qualitative one.

c) For the pie chart, we need the frequency of the pair's of the jeans according to which state they were produced in.

California, CA, frequency = 9

Arizona, AZ, frequency = 8

Texas, TX, frequency = 8

Total = 25

A pie chart is based on 360°

CA will occupy (9/25) × 360° = 129.6°

AZ will occupy (8/25) × 360° = 115.2°

TX will occupy (8/25) × 360° = 115.2°

The pie chart is drawn with Microsoft Excel and presented in the image attached to this answer.

d) The bar chart is drawn with Microsoft Excel and presented in the image attached to this question. Each bar has equal width, but the height of each bar corresponds to its frequency.

e) The proportion of jeans produced in Texas = 8/25 = 0.32

f) The state that produces the highest number of jeans is the one with the highest frequency. That is California with frequency of 9 out of 25.

(g) The plant that produced more jeans than the others is the state in the

pie chart of part (c) with the largest angle (129.6°) or slice (California) and is the state in the bar graph of part (d) that has the highest bar.

From the data, it is evident that the three states make almost the same number of jeans, but California slightly edges the other two by being the state that produces the most number of jeans. Arizona and Texas produce the similar amounts of Jeans.

Although, this is just a sample out of a whole large quantity of Jeans, the laws of statistics and probability makes this random selection a representative of the whole set of jeans produced.

Hope this helps!