Answer to Question #234632 in Statistics and Probability for ZONKE

Question

A random sample of 100 bags of potatoes found that the sample mean X for the weight of the bags

was 10.2 kilograms. Assume that the population variance of the weights is known to be 2.5 kg.

(a) Compute an unbiased point estimate for the population mean : (3)

(b) Find the standard error of the mean. (3)

(c) Find the 90% and 99% confidence intervals for the population mean, : (10)

(d) Explain what the 99% confidence interval tells us about the population mean, :

Answer 1

(a) $\bar x=10.2.$

(b) $SE=\frac{\sigma}{\sqrt{n}}=\frac{2.5}{\sqrt{100}}=0.25.$

(c) $90\%CI=(10.2-1.645*0.25, 10.2+1.645*0.25)=(9.789,10.611).$

$99\%CI=(10.2-2.576*0.25,10.2+2.476*0.25)=(9.556,10.844).$

(d) We are 99% confident that the population average weight of the bags lies between 9.556 kg

and 10.844 kg.