The Kent City Health Department is interested in estimating the mean number of c

Question

The Kent City Health Department is interested in estimating the mean number of cockroaches per apartment at the College Towers apartment complex. They randomly sample 22 apartments in the complex which results in a sample mean number of cockroaches of 289 with a standard deviation of 33. Given that there are 540 apartments in the complex, construct a 95% confidence interval for the mean number of cockroaches per apartment. Interpret your interval (i.e. what, exactly, does it mean in this case). Round to 4 (four) quality decimal places.

Explanation / Answer

Answer to the question:

The Xbar = 289

Z = 1.96 for 95% CI

Also, n=22 and sigma = 33

Inputting in CI formula we have:

289 +/- 1.96*33/sqrt(22)

=275.21 to 302.79

It is interpreted as " A 95%confidence interval has a 0.95 probability of containing the population mean. The range of that is from 275.21 to 302.79"

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