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:
- Normal populations - as stated, we can assume that the differences (self-reported minus measured) are normally distributed.
- Paired samples - the analysis is based on the paired differences for the same individuals (self-report vs. measured).
- 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.
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