Question

Son's Height   Father's Height
64.4 79
69.2 67.1
76.4 70.9
69.2 66.8
78.2 72.8
76.9 70.4
71.8 70.3
79 70.1
75.8 79.5
72.3 65.5
69.2 65.4
66.9 69.1
64.5 74.5

To test the claim that sons are taller than their fathers on average, a researcher randomly selected 13 fathers who have adult male children.  She records the height of both the father and son in inches.  

Note: to answer the questions below, subtract (Son’s Height – Father’s Height).

1. What is (are) the parameter(s) of interest?  Choose one of the following symbols m(the population mean);m_D(the mean difference from paired (dependent) data);m₁- m₂ (the difference of two independent means) and describe the parameter in context of this question in one sentence.

2. Depending on your answer to part (a), construct one or two relative frequency histograms.  Remember to properly title and label the graph(s).  Copy and paste these graphs into your document.

3. Describe the shape of the histogram(s) in one sentence.

4. Depending on your answer to part (a), construct one or two boxplots and copy and paste these graphs into your document.

5. Does the boxplot (or do the boxplots) show any outliers?  Answer this question in one sentence and identify any outliers if they are present.

6. Considering your answers to parts (c) and (e), is inference appropriate in this case?  Why or why not?  Defend your answer using the graphs in two to three sentences.

Answer 1

The histogram for Son's Height is:

The histogram for Father's Height is:

The boxplot for Son's Height is:

The boxplot for Father's Height is:

No outliers.

The hypothesis being tested is:

H₀: m₁- m₂ = 0

H₁: m₁- m₂ ≠ 0

The output is:

Son's Height	Father's Height
71.831	70.877	mean
5.071	4.576	std. dev.
13	13	n
	24	df
	0.9538	difference (Son's Height - Father's Height)
	23.3263	pooled variance
	4.8297	pooled std. dev.
	1.8944	standard error of difference
	0	hypothesized difference
	0.504	t
	.6192	p-value (two-tailed)

Since the p-value (0.6192) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that the mean difference is not equal for both groups.