Question

Listed below are body temperatures from five different subjects measured at 8 AM and again at 12 AM. Find the values of d overbar and s Subscript d. In​ general, what does mu Subscript d ​represent? Temperature (degrees Upper F )at 8 AM 97.8 98.7 97.3 97.5 97.2 Temperature (degrees Upper F )at 12 AM 98.3 99.3 97.6 97.4 97.6 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 overbar and s Subscript d.\

Answer 1

Answer:

$(a)\bar {d} =-0.34\\(b)s_{d}=0.073$

Step-by-step explanation:

$\left|\begin{array}{c|c|c} Temperature at 8 AM & Temperature at 12 AM & Difference \\---------&--------&------\\97.8&98.3&-0.5\\98.7&99.3&-0.6\\97.3&97.6&-0.3\\97.5&97.4& 0.1\\97.2&97.6&-0.4\end{array}\right|$

(b)

$\bar {d} is the sample mean of all the difference in temperature \\\bar {d} =\dfrac{-0.5-0.6-0.3+0.1-0.4}{5} =\dfrac{-1.7}{5} =-0.34$

(c)$s_{d} is the standard deviation of all the difference in temperature$

$(-0.5-(-0.34))^{2}=0.0256\\(-0.6-(-0.34))^{2}=0.0676\\(-0.3-(-0.34))^{2}=0.0016\\(0.1-(-0.34))^{2}=0.1936\\(-0.4-(-0.34))^{2}=0.0036\\s_{d} =\dfrac{0.0256+0.0676+0.0016+0.1936+0.0036}{5-1}=\dfrac{0.292}{4}\\s_{d}=0.073$

(d)$\mu_d$ represents the mean of the difference in body temperature at 8AM and 12AM of the population of all people.