Question

directions: show all your work. indicate clearly the methods you use, because you will be scored on the correctness of your methods as well as on the accuracy and completeness of your results and explanations. a university researcher is interested in comparing the percents of high school seniors who took a college entrance exam for two different regions of the country, region i and region ii. the researcher recorded the percent of seniors taking the exam for each high school within the two regions. the boxplots of the distributions of the percents of seniors who took the college entrance exam are shown below. a. compare the distributions of percents of seniors who took the college entrance exam for the two regions. b. in writing a report, the researcher produced a single histogram of the combined data for region i and region ii. describe the shape of the histogram for the combined data.

Explanation:

Step1: Analyze box - plots for distribution comparison

For Region I, the box - plot shows a right - skewed distribution as the right whisker is longer and the median is closer to the first quartile. The values range from approximately 60 to 90 with the median around 75. For Region II, the box - plot is left - skewed as the left whisker is long and the median is closer to the third quartile. The values range from approximately 0 to 20 with a median around 10.

Step2: Consider combined data for histogram shape

Since Region I has values mainly in the 60 - 90 range and Region II has values mainly in the 0 - 20 range, when combined, the histogram will be bimodal. There will be two peaks, one around the 0 - 20 range (from Region II) and one around the 60 - 90 range (from Region I).

Answer:

a. Region I has a right - skewed distribution with values ranging from about 60 to 90 and median around 75. Region II has a left - skewed distribution with values ranging from about 0 to 20 and median around 10.
b. The histogram of the combined data will be bimodal.