Question

Astronauts increased in height by an average of approximately 40 mm (about an inch and a half)during theApollo-Soyuzmissions, due to the absence of gravity compressing their spines duringtheir time in space. Does something similar happen here on Earth? An experiment supported byNASA measured the heights of six men immediately before going to bed, and then again after threedays of bed rest (Styf et al. 1997). On average, they increased in height by 14 mm, with standarddeviation 0.66 mm. Find the 95% confidence interval for the change in height after three days ofbed rest.

Answer 1

Answer:

The 95​% confidence interval estimate for the change in height after three days of bed rest is (13.306mm, 14.694mm).

Step-by-step explanation:

Our sample size is 6.

The first step to solve this problem is finding our degrees of freedom, that is, the sample size subtracted by 1. So

$df = 6-1 = 5$

Then, we need to subtract one by the confidence level $\alpha$ and divide by 2. So:

$\frac{1-0.95}{2} = \frac{0.05}{2} = 0.025$

Now, we need our answers from both steps above to find a value T in the t-distribution table. So, with 5 and 0.025 in the t-distribution table, we have $T = 2.571$.

Now, we find the standard deviation of the sample. This is the division of the standard deviation by the square root of the sample size. So

$s = \frac{0.66}{\sqrt{6}}} = 0.27$

Now, we multiply T and s

$M = T*s = 2.571*0.27 = 0.694$

For the lower end of the interval, we subtract the mean by M. So $14 - 0.694 = 13.306$

For the upper end of the interval, we add the mean to M. So $14 + 0.694 = 14.694$

The 95​% confidence interval estimate for the change in height after three days of bed rest is (13.306mm, 14.694mm).