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

Answer:

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

(1.2878 ,1.9122)

Step-by-step 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

$(x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } , x^{-} - t_{\frac{\alpha }{2} } \frac{S}{\sqrt{n} } )$

$(1.6 - 2.618 \frac{0.43}{\sqrt{13} } , 1.6 - 2.618 \frac{0.43}{\sqrt{13} } )$

( 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)