Math / Data & Statistics

QuestionThe electric cooperative needs to know the mean household usage of electricity by its non-commercial customers in kWh per day. Assume that the population standard deviation is 2.5 kWh . The mean electricity usage per family was found to be 17.7 kWh per day for a sample of 443 families. Construct the $80 \%$ confidence interval for the mean usage of electricity. Round your answers to one decimal place.

Studdy Solution
Construct the confidence interval using the formula:
$\bar{x} \pm \text{ME}$
Substitute the values:
$17.7 \pm 0.152$
Calculate the interval:
$(17.7 - 0.152, 17.7 + 0.152)$
$(17.5, 17.9)$
Round to one decimal place:
$(17.5, 17.9)$
The $80\%$ confidence interval for the mean usage of electricity is:
$\boxed{(17.5, 17.9)}$

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