Question

You want to estimate the mean weight of quarters in circulation. A sample of 60 quarters has a mean weight of 5.625 grams and a standard deviation of 0.063 gram. Use a single value to estimate the mean weight of all quarters.​ Also, find the​ 95% confidence interval for the average weight of all quarters.

The estimate for the mean weight of all quarters is ___ grams?

Answer 1

The estimate for the mean weight of all quarters is $5.625$ grams.

The critical value for $\alpha=0.05$ and $df=n-1=60-1=59$ degrees of freedom is $t_c=z_{1-\alpha/2, n-1}=2.000995.$ The corresponding confidence interval is computed as shown below:

$$CI=(\bar{x}-t_c\times\dfrac{s}{\sqrt{n}}, \bar{x}+t_c\times\dfrac{s}{\sqrt{n}})$$ $$=(5.625-2.000995\times\dfrac{0.063}{\sqrt{60}},$$

$$5.625+2.000995\times\dfrac{0.063}{\sqrt{60}})$$

$$=(5.608725, 5.641275$$

Therefore, based on the data provided, the 95% confidence interval for the population mean is $5.609<\mu<5.641,$ which indicates that we are 95% confident that the true population mean $\mu$ is contained by the interval $(5.609, 5.641).$