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Question 26, 9.3.21-T
HW Score: of 30 points
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Supposedly, a person’s height is approximately equal to their arm span. Refer the “ANSUR II 2012” data in the accompanying table and use the heights and arm spans ( mm ) of the 127 males. Use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal. Use a 0.01 significance level to test the claim that for males, their height is the same as their arm span.

Click the icon to view the data from ANSUR II 2012.

In this example, is the mean value of the differences for the population of all pairs of data, where each individual difference is defined as the arm span minus the height. What are the null and alternative hypotheses for the hypothesis test?

(Type integers or decimals. Do not round.)
Identify the test statistic.
(Round to two decimal places as needed.)

Ask by Washington Moreno. in the United States

Mar 31,2025

Question

Test 5 Review
Question 26, 9.3.21-T
HW Score: of 30 points
Save

Supposedly, a person’s height is approximately equal to their arm span. Refer the “ANSUR II 2012” data in the accompanying table and use the heights and arm spans ( mm ) of the 127 males. Use the listed paired sample data, and assume that the samples are simple random samples and that the differences have a distribution that is approximately normal. Use a 0.01 significance level to test the claim that for males, their height is the same as their arm span.

Click the icon to view the data from ANSUR II 2012.

In this example, is the mean value of the differences for the population of all pairs of data, where each individual difference is defined as the arm span minus the height. What are the null and alternative hypotheses for the hypothesis test?

(Type integers or decimals. Do not round.)
Identify the test statistic.
(Round to two decimal places as needed.)

Ask by Washington Moreno. in the United States

Mar 31,2025

UpStudy AI · Accepted Answer

**Step 1. Define the Differences**

Let each individual difference be defined as  
$$
d = \text{arm span} - \text{height}.
$$
Then the mean difference for the population is $$ \mu_d $$.

**Step 2. State the Hypotheses**

The null and alternative hypotheses for testing whether a male’s height is equal to his arm span are

$$
\begin{aligned}
H_{0}: &\quad \mu_d = 0 \quad \text{mm,} \
H_{1}: &\quad \mu_d \neq 0 \quad \text{mm.}
\end{aligned}
$$

**Step 3. Choose the Test and Write the Test Statistic**

Because we have paired data and we assume the differences are approximately normally distributed, we use the paired $$ t $$-test. The test statistic is given by

$$
t = \frac{\bar{d} - \mu_0}{s_d / \sqrt{n}},
$$

where  
$$\bar{d}$$ = sample mean of the differences,  
$$s_d$$ = sample standard deviation of the differences,  
$$n = 127$$ (the sample size), and  
$$\mu_0 = 0$$ (the hypothesized mean difference).

Thus, the test statistic simplifies to

$$
t = \frac{\bar{d}}{s_d / \sqrt{127}}.
$$

This is the formula you would use to compute the test statistic, rounding to two decimal places as required.
**Hypotheses:** - $$ H_{0}: \mu_d = 0 $$ mm - $$ H_{1}: \mu_d \neq 0 $$ mm **Test Statistic:** $$ t = \frac{\bar{d}}{s_d / \sqrt{127}} $$

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