Drug concentrations: A sample of 10 people ingested a new formulation of a drug. Six hours later, the concentrations in their bloodstreams, in nanograms per milliliter, were as follows:

1.2, 3.2, 2.5, 1.5, 3.1, 2.7, 1.3, 4.1, 1.1, 2.2

Part 1 of 2
(a) Construct a dotplot for the given sample.

Part 2 of 2
(b) Is it reasonable to treat the sample as coming from an approximately normal population? Explain.

Yes
No

To answer this question, we need to construct a dotplot for the data and then assess if it's reasonable to treat the sample as coming from an approximately normal population.
Part 1 of 2(a): Constructing a Dotplot
A dotplot is a simple way to display numerical data where each value is shown as a dot above its corresponding place on a number line. Let's construct a dotplot for the concentrations (in nanograms per milliliter): 1.2, 3.2, 2.5, 1.5, 3.1, 2.7, 1.3, 4.1, 1.1, 2.2.

Identify the Range:

Smallest Value: 1.1
Largest Value: 4.1


Create a Number Line:

Create a horizontal line with labeled values from 1.0 to 4.5, with increments of 0.5.


Plot Each Data Point:

Place a dot above the number line at each data point. If multiple data points have the same value, stack the dots vertically.



Here is a simplified representation:
4.0 | * 3.5 | 3.0 | * * 2.5 | * * 2.0 | * * 1.5 | * * 1.0 | * *
Part 2 of 2(b): Checking for Normality
To determine if it's reasonable to treat this sample as coming from an approximately normal population, we can look for signs of symmetry and the presence of a bell-shaped distribution in the dotplot.

Assess Symmetry:

Ideally, a normal distribution will be symmetric around a central peak. In this dotplot, while there is some symmetry, there is not a clear central peak due to the small sample size.


Sample Size Consideration:

With a larger sample size, normality can be assessed more accurately. A sample of 10 is relatively small, which makes it harder to confidently judge the distribution's normality.



In conclusion, No , it might not be completely reasonable to treat this small sample as coming from an approximately normal population just based on visual inspection. Statistical tests or a larger sample might be needed for better insight. However, if other statistical methods or testing tools suggest normality and for educational purposes, assuming approximate normality isn't uncommon with small samples in practice.

Answered by JessicaJessy | 2025-07-06