Answer:
It is 80% statistically safe to conclude that the population standard deviation is less than 1.8°F
Step-by-step explanation:
The given information are;
The sample size, n = 102
The sample mean = 98.4°F
The sample standard deviation = 0.66°F
[tex]\sqrt{\dfrac{\left (n-1 \right )s^{2}}{\chi _{\alpha /2}^{}}}< \sigma < \sqrt{\dfrac{\left (n-1 \right )s^{2}}{\chi _{1-\alpha /2}^{}}}[/tex]
α = 0.2, ∴ α/2 = 0.1
[tex]\chi _{1-\alpha /2}[/tex] = [tex]\chi _{0.9, 101}[/tex] = 83.267
[tex]\chi _{\alpha /2}[/tex] = [tex]\chi _{0.1, 101}[/tex] = 119.589,
Which gives;
[tex]\sqrt{\dfrac{\left (102-1 \right )0.66^{2}}{119.589}^{}}}< \sigma < \sqrt{\dfrac{\left (102-1 \right )0.66^{2}}{83.267}^{}}}[/tex]
0.607 < σ <0.727
Therefore, it is 80% statistically safe to conclude that the population standard deviation is less than 1.8°F.
