Question

A study was commissioned to find the mean weight of the residents in certain town.The study examined a random sample of 37 residents and found the mean weight tobe 158 pounds with a standard deviation of 27 pounds. Determine a 95% confidenceinterval for the mean, rounding all values to the nearest tenth.

Answer 1

We know that the sample n= 37, the mean is 158 and standard deviation is 27. At 95% confidence the interval is given by

`\bar{x}\pm z*\frac{\sigma}{\sqrt[]{n}}`

where z is equal to 1.96. By substituting the given values into this formula, we get

`158\pm(1.96)\frac{27}{\sqrt[]{37}}`

Then, the interval is

`158\pm8.699`

Finally, by rounding up to the nearest tenth, the interval is

`\begin{gathered} 158\pm8.7 \\ or \\ 149.3\le158\le166.7 \end{gathered}`

The value for z at 95% confidence is given in the followin table: