Question

9. A simple random sample of 37 weights of pennies made after 1983 has a sample mean of 2.4991 g and a known population standard deviation of 0.0165 g.

a. Construct a 99% confidence interval estimate of the mean weight of all such pennies.

b. Design specifications require a population mean of 2.5 g. What does the confidence interval suggest about the manufacturing process?

10. A random sample of 40 students has a mean annual earnings of $3120 and a known standard deviation of $677 from a previous study. a. What is the best point estimate for the population mean? b. If we want to create a 99% confidence interval, what is the margin of error? c. Construct the 99% confidence interval.

Answer 1

9)

a)

z value at 99% = 2.576

CI = mean +/- z *(s/sqrt(n))

= 2.4991 +/- 2.576 *(0.0165/sqrt(37))
= (2.4921 , 2.5061)

b)
The confidence interval suggests that the Do not reject H0 as confidence interval contain population mean 2.5

10)
a)

Point estimate = 3120

b)
Margin of error = z*(s/sqrt(n))
z value at 99% = 2.576

= 2.576 *(677/sqrt(40))
= 275.743

c)

CI = mean +/- ME
= 3120 +/- 275.743
= (2844.2570 , 3395.7430)