Answer :
The values are:
d = 0.64
Sd = 1.43
Ha represents the alternative hypothesis in statistical hypothesis testing.
Given data:
Temperature (°F) at 8 AM: 97.9, 99.4, 99.7, 97.4, 97.6
Temperature (°F) at 12 AM: 98.5, 97.1, 97.3, 97.5, 97.4
Let's calculate the differences:
d (mean of the differences):
[tex]d = \frac{\sum (X_i - Y_i)}{n}[/tex]
Xi is the temperature at 8 AM,
Yi is the temperature at 12 AM, and
n is the number of pairs.
[tex]d = \frac{(97.9 - 98.5) + (99.4 - 97.1) + (99.7 - 97.3) + (97.4 - 97.5) + (97.6 - 97.4)}{5}[/tex]
[tex] d = \frac{-0.6 + 2.3 + 2.4 - 0.1 + 0.2}{5}[/tex]
[tex]d = \frac{3.2}{5} = 0.64[/tex] rounded to two decimal places
Sd standard deviation of the difference
[tex]Sd = \sqrt{\frac{\sum (X_i - Y_i - d)^2}{n-1}}[/tex]
Where
d is the mean of the differences.
[tex]Sd = \sqrt{\frac{(-0.6 - 0.64)^2 + (2.3 - 0.64)^2 + (2.4 - 0.64)^2 + (-0.1 - 0.64)^2 + (0.2 - 0.64)^2}{4}}[/tex]
[tex] Sd = \sqrt{\frac{(-1.24)^2 + (1.66)^2 + (1.76)^2 + (-0.74)^2 + (-0.44)^2}{4}}[/tex]
[tex]Sd = \sqrt{\frac{1.5376 + 2.7556 + 3.0976 + 0.5476 + 0.1936}{4}}[/tex]
[tex]Sd = \sqrt{\frac{8.132}{4}} = \sqrt{2.033} \approx 1.43[/tex]rounded to two decimal places
So, the values are:
d = 0.64
Sd = 1.43
In general, Ha represents the alternative hypothesis in statistical hypothesis testing. It usually states what we suspect is true about a population parameter when we reject the null hypothesis.
