Question

Jacy wants to determine how age and height are related to shoe preference in her town. She selects a simple

random sample of 25 individuals taller than five feet seven inches from the 18-to 21-year age group and records
their age, height, and shoe preference (tennis shoes, high-heeled shoes, sandals). She also selects an independent
simple random sample of 30 individuals shorter than five feet seven inches from the 35-to 45-year age group and
records the same information. Which is the most important observation about Jacy's plan?
Her samples are too small.
She should have used equal sample sizes.
The plan is well conceived and should serve the intended purpose.
She will be unable to tell whether a difference in shoe preference is related to a difference in age or to a
difference in height.
She should have selected the two age groups randomly instead of choosing them specifically.

Answer 1

She will be unable to tell whether a difference in shoe preference is related to a difference in age or to a difference in height.

Explanation:

In this study she selected the first sample for individuals taller than five feet seven inches from the 18-to 21-year age group.In the second sample, the individuals selected were shorter than five feet seven inches from the 35-to 45-year age group. You see here, the second sample could have been in the age group similar to the first one because "age" itself could be a factor that affects shoe preference. For the difference heights in the two samples is okay because she can identify which individuals tall or short prefere a certain shoe.