A survey of 71
randomly selected homeowners finds that they spend a mean of $63
per month on home maintenance. Construct a 98%
confidence interval for the mean amount of money spent per month on home maintenance by all homeowners. Assume that the population standard deviation is $12
per month. Round to the nearest cent.
Using the formula for calculating a confidence interval for the population mean when the population standard deviation is known:
CI = x̄ ± Z*(σ/√n)
Where:
CI = Confidence Interval
x̄ = sample mean = $63
Z = Z-score for 98% confidence interval = 2.33
σ = population standard deviation = $12
n = sample size = 71
Plugging in the values:
CI = 63 ± 2.33*(12/√71)
CI = 63 ± 2.33*(1.43)
CI = 63 ± 3.33
CI = (59.67, 66.33)
Therefore, the 98% confidence interval for the mean amount of money spent per month on home maintenance by all homeowners is $59.67 to $66.33.