Question

In a random sample of 12 residents of Brooksville the mean waste recycled per person was 1.3 pound with a standard deviation of 0.25 pounds. What is the 80% confidence interval for the mean waste recycled per person?

Answer 1

Answer on Question #44385 – Math - Statistics and Probability

Problem.

In a random sample of 12 residents of Benton the mean waste recycled per person was 1.3 pound with a standard deviation of 0.25 pounds. What is the 80% confidence interval for the mean waste recycled per person?

Solution.

Assume the population standard deviation is known.

Therefore, $z^*$-value for 80% confidence level equals $z^* = 1.28$.

If $n = 12$ is number of residents, $\bar{x} = 1.3$ is mean and $\sigma = 0.25$ then the confidence interval for mean waste recycled per person is

$$\left(\bar {x} - z ^ {*} \frac {\sigma}{\sqrt {n}}; \bar {x} + z ^ {*} \frac {\sigma}{\sqrt {n}}\right).$$

and equals

$$\left(1.3 - 1.28 \cdot \frac {0.25}{\sqrt {12}}; 1.3 + 1.28 \cdot \frac {0.25}{\sqrt {12}}\right), \text{ i.e. } (1.208; 1.392).$$

Answer: (1.208; 1.392).

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