To find: The confidence interval for the mean population.

Question
Confidence intervals
asked 2021-01-08
To find: The confidence interval for the mean population.

Answers (1)

2021-01-09
The total size of the sample of the high school athletes is 233. The meanof the times they spend on the practicing is 1.6 h and the standard deviation is 0.5 h. Obtain the z-value from the z-table of \(\displaystyle{99}\%\) confidence corresponding to the given mean and standard deviation is 2.576. The confidence interval for the mean populationis calculated as, \(\displaystyle{C}=\ \overline{{{x}}}\ \pm\ {z}\ \times\ {\frac{{{s}}}{{\sqrt{{{n}}}}}}\)
\(\displaystyle={1.6}\ \pm\ {\left({2.576}\right)}\ {\left({\frac{{{0.5}}}{{\sqrt{{{233}}}}}}\right)}\)
\(\displaystyle={1.6}\ \pm\ {0.0084}\)
\(\displaystyle={1.516},\ {1.684}\) Thus, the confidence interval for the mean population is \(\displaystyle{1.516}\ \leq\ \mu\ \leq\ {1684}.\)
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