We have to find the minimum sample size.
The margin of error that it is aimed is ±0.2 hours from the real mean.
The population standard deviation is 0.8 hours.
The desired level of confidence is 96%. This corresponds to a z-score of 2.054.
We can relate sample size with the given information as:
[tex]\begin{gathered} e=\frac{\sigma}{\sqrt{n}}\cdot z \\ \sqrt{n}=\frac{\sigma}{e}\cdot z \\ n=(\frac{\sigma\cdot z}{e})^2 \end{gathered}[/tex]If we replace e = 0.2, σ = 0.8 and z = 2.054 we can calculate the sample size n as:
[tex]\begin{gathered} n=(\frac{0.8*2.054}{0.2})^2 \\ \\ n=(8.216)^2 \\ n\approx67.5 \\ n\approx68 \end{gathered}[/tex]Answer: the sample size has to be at least 68 people.
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