Question

In a random sample of 12 residents of the state of Montana, the mean waste recycled per person per day was 1.0 pounds with a standard deviation of 0.65 pounds. Determine the 95% confidence interval for the mean waste recycled per person per day for the population of Montana. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answer 1

Answer:

The 95% confidence interval for the mean waste recycled per person per day for the population of Montana.

(0.58701 , 1.41299)

Step-by-step explanation:

Step:-1

Given that the size of the sample 'n' =12

Given that mean of the sample x⁻ = 1.0 pounds

Given that the standard deviation of the sample (S) = 0.65 pounds

Step:- 2

The 95% confidence interval for the mean waste recycled per person per day for the population of Montana.

$(x^{-} - t_{0.05} \frac{S.D}{\sqrt{n} } , x^{-} + t_{0.05} \frac{S.D}{\sqrt{n} } )$

$(1.0 - 2.2010 \frac{0.65}{\sqrt{12} } , 1.0 + 2.2010 \frac{0.65}{\sqrt{12} } )$

(1.0 - 0.41299 , 1.0 + 0.41299)

(0.58701 , 1.41299)

Final answer:-

The 95% confidence interval for the mean waste recycled per person per day for the population of Montana.

(0.58701 , 1.41299)