Question

d?

sd?

what does ud represent?

Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of d and . In general, what does represent? Temperature (°F) at 8 AM 97.8 Temperature (°F) at 12 AM 98.3 98.8 99.4 97.8 982 97.7 97.4 97.8 982 Let the temperature at 8 AM be the first sample, and the temperature at 12 AM be the second sample. Find the values of d and Type an integer or a decimal. Do not round)

Answer 1

xi : Body Temperature of ith subject at 8AM

yi : Body Temperature of ith subject at 12AM

di: Difference in body temperatures measured at 8 AM and again at 12AM (xi -yi) of ith subject in the sample (i=1,2,3,4,5)

sample size : Number of subjects : n=5

$\overline{d}$ : Sample mean difference in body temperatures measured at 8 AM and again at 12AM

sd : Sample standard deviation of difference in body temperatures measured at 8 AM and again at 12AM

$\overline{d}=\frac{\sum_{i=1}^{n} d_{i}}{n}=\frac{\sum_{i=1}^{5} d_{i}}{5}$

$s_{d}=\sqrt{}\frac{\sum_{i=1}^{n}(d_{i}-\overline{d})^{2}}{n-1}=\sqrt{}\frac{\sum_{i=1}^{5}(d_{i}-\overline{d})^{2}}{5-1}$

xiTemperature at 8AM	yi:Temperaturea at 6AM	di = xi-yi	$\small d_{i}-\overline{d}$	(P - !p)
97.8	98.3	-0.5	-0.18	0.0324
98.8	99.4	-0.6	-0.28	0.0784
97.8	98.2	-0.4	-0.08	0.0064
97.7	97.4	0.3	0.62	0.3844
97.8	98.2	-0.4	-0.08	0.0064
		$\small \Sigma d_{i}=-1.6$		$\small \Sigma (d_{i}-\overline{d})^{2}=0.508$
		$\small \overline{d}=-0.32$

$\overline{d}=\frac{\sum_{i=1}^{5} d_{i}}{5}=\frac{-1.6}{5}=-0.32$

$s_{d}=\sqrt{\frac{\sum_{i=1}^{5}(d_{i}-\overline{d})^{2}}{5-1}}=\sqrt{\frac{0.508}{4}}=\sqrt{0.127}=0.356370594$

$\overline{d}=-0.32$

$s_{d}=0.356370594$

$\mu _{d}$ : represents the Population mean difference in body temperatures measured at 8 AM and again at 12AM