Answer :
Answer:
[tex](a)\bar {d} =-0.34\\(b)s_{d}=0.073[/tex]
Step-by-step explanation:
[tex]\left|\begin{array}{c|c|c}$Temperature at 8 AM${data-answer}amp;$Temperature at 12 AM${data-answer}amp;$Difference$\\---------&--------&------\\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|[/tex]
(b)
[tex]\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[/tex]
(c)[tex]s_{d} $ is the standard deviation of all the difference in temperature$[/tex]
[tex](-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[/tex]
(d)[tex]\mu_d[/tex] represents the mean of the difference in body temperature at 8AM and 12AM of the population of all people.
The sample means of the difference in temperature will be -0.34.
How to calculate the mean?
The sample means of the difference in temperature will be calculated thus:
= (-0.5 - 0.6 - 0.3 +0.1 - 0.4) / 5
= -1.7/5
= -0.34
Also, the standard deviation will be:
= (0.0256 + 0.0676 + 0.0016 + 0.1936 + 0.0036) / (5-1)
= 0.073
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