Math / Data & Statistics

QuestionIn a random sample of 16 residents of the state of Washington, the mean waste recycled per person per day was 2.8 pounds with a standard deviation of 0.24 pounds. Determine the $80 \%$ confidence interval for the mean waste recycled per person per day for the population of Washington. Assume the population is approximately normal.
Step 2 of 2: Construct the $80 \%$ confidence interval. Round your answer to one decimal place.
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Lower endpoint: $\square$ Upper endpoint: $\square$

Studdy Solution
Construct the confidence interval:
$\text{Lower endpoint} = \bar{x} - ME = 2.8 - 0.08046 \approx 2.7$
$\text{Upper endpoint} = \bar{x} + ME = 2.8 + 0.08046 \approx 2.9$
Round to one decimal place:
$\text{Lower endpoint} = 2.7, \quad \text{Upper endpoint} = 2.9$
The $80\%$ confidence interval for the mean waste recycled per person per day is:
$(2.7, 2.9)$

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