Question

In a random sample of 13 residents of the state of Washington, the mean waste recycled per person per day was 1.6 pounds with a standard deviation of 0.43 pounds. Determine the 98% confidence interval for the mean waste recycled per person per day for the population of Washington. 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

The 98% confidence interval for the mean waste recycled per person per day for the population of Washington

(1.2878 ,1.9122)

Explanation:

Step(i):-

Given random sample size 'n' = 13

The mean waste recycled per person per day

x⁻ = 1.6 pounds

The standard deviation of the sample 's' = 0.43 pounds

Degrees of freedom

ν = n-1 = 13 -1 =12

t₀.₀₁ = 2.618

step(ii):-

The 98% confidence interval for the mean waste recycled per person per day for the population of Washington

`(x^(-) - t_{(\alpha )/(2) } (S)/(√(n) ) , x^(-) - t_{(\alpha )/(2) } (S)/(√(n) ) )`

`(1.6 - 2.618 (0.43)/(√(13) ) , 1.6 - 2.618 (0.43)/(√(13) ) )`

( 1.6 - 0.3122 , 1.6 +0.3122)

(1.2878 ,1.9122)

Final answer:-

The 98% confidence interval for the mean waste recycled per person per day for the population of Washington

(1.2878 ,1.9122)