Question

As part of the National Health and Nutrition Examination Survey, the Department of Health and Human Services obtained self-reported heights and measured heights for males aged 12—16. You may also assume that the samples are from normal populations. All measurements are in inches. Listed below are sample results.

Male Reported Height (inches) Measured Height (inches) Difference (inches)
1 63.4 63.6 -0.2
2 65.9 64.7 1.2
3 62.7 62.9 -0.2
4 66.7 66.7 0
5 61.1 61.4 -0.3
6 62.5 62.3 0.2
7 61.7 60.2 1.5
8 61.9 62 -0.1
9 62 60.6 1.4
10 65.6 65.3 0.3
Sample average

63.35 62.97 0.38
Standard Deviation 1.99 2.11 0.71
Use 5% level of significance to decide whether there is sufficient evidence that the self-reported average male height is greater than the measured average male height.

Procedure:
Select an answer

Assumptions: (select everything that applies)

Population standard deviations are known
Normal populations
Simple random samples
Population standard deviation are unknown but assumed equal
Paired samples
Sample sizes are both greater than 30
The number of positive and negative responses are both greater than 10 for both samples
Independent samples
Population standard deviation are unknown

Answer 1

To determine whether there is sufficient evidence that the self-reported average male height is greater than the measured average male height, we need to set up and perform a hypothesis test. The hypotheses for this test can be formulated as follows:

- **Null Hypothesis (H0):** \( \mu_d \leq 0 \) (The average self-reported height is less than or equal to the average measured height)
- **Alternative Hypothesis (H1):** \( \mu_d > 0 \) (The average self-reported height is greater than the average measured height)

Where \( \mu_d \) is the mean difference between self-reported height and measured height.

Given the data provided, we need to identify the relevant assumptions for conducting the test.

Assumptions:
1. **Normal populations** - as stated, we can assume that the differences (self-reported minus measured) are normally distributed.
2. **Paired samples** - the analysis is based on the paired differences for the same individuals (self-report vs. measured).
3. **Population standard deviation are unknown** - in this case, we are dealing with sampled data and the population parameter is not known.

Based on these points, the applicable assumptions are:

- **Normal populations**
- **Paired samples**
- **Population standard deviation are unknown**

Thus, these three assumptions apply to the hypothesis test regarding male heights in this context.