QuestionFind the confidence interval for the true mean weight given a mean of 167 pounds and a margin of error of 3 pounds.

Studdy Solution

STEP 1

Assumptions1. The mean weight of the residents in the town is167 pounds. . The margin of error for the mean weight is3 pounds.
3. We are asked to find a confidence interval, which is a range of values that is likely to contain the true mean weight.

STEP 2

A confidence interval is calculated using the formula $Confidence\, Interval = Mean \pm Margin\, of\, Error$

STEP 3

Now, plug in the given values for the mean weight and the margin of error to calculate the confidence interval.
$Confidence\, Interval =167 \pm3$

STEP 4

To find the lower limit of the confidence interval, subtract the margin of error from the mean.
$Lower\, Limit = Mean - Margin\, of\, Error$

STEP 5

Plug in the values for the mean weight and the margin of error to calculate the lower limit.
$Lower\, Limit =167 -3$

STEP 6

Calculate the lower limit of the confidence interval.
$Lower\, Limit =167 -3 =164$

STEP 7

To find the upper limit of the confidence interval, add the margin of error to the mean.
$Upper\, Limit = Mean + Margin\, of\, Error$

STEP 8

Plug in the values for the mean weight and the margin of error to calculate the upper limit.
$Upper\, Limit =167 +3$

STEP 9

Calculate the upper limit of the confidence interval.
$Upper\, Limit =167 +3 =170$ The confidence interval for the true mean weight of the residents of the town is from164 pounds to170 pounds.

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