Answer
i) $22.5 < \mu < 25.7$ We are 90% confident that the population mean length of time falls between 22.5 and 25.7 minutes.
ii) $21.6 < \mu < 26.6$. We are 99% confident that the population mean length of time falls between 21.6 and 22.6 minutes.
iii) The 99% Confidence interval is wider.
Work Step by Step
i) The sample mean is 24.1
ii)
= $24.1 \pm ( 1.645\times\frac{4.3}{\sqrt20})$
= $24.1\pm 1.5817$
CI: $ 22.5183 < \mu < 25.6817 \approx 22.5 < \mu < 25.7$
We are 90% confident that the population mean length of time falls between 22.5 and 25.7 minutes.
iii)
= $24.1 \pm ( 2.5758\times\frac{4.3}{\sqrt20})$
= $24.1\pm 2.4767$
CI: $ 21.6233 < \mu < 26.5767 \approx 21.6 < \mu < 26.6$
We are 99% confident that the population mean length of time falls between 21.6 and 22.6 minutes.
iv)
The 99% Confidence interval is wider.
