Question

1) A random sample of the number of hours worked by 40 employees has a mean of 29.6 hours worked. Assume the population standard deviation is 7.9 hours.

a. Using a 95% confidence level, find the margin of error, E, for the mean number of hours worked.

2) In a study of 265 subjects, the average score on the examination was 63.8. Assume σ = 3.08.

a. What is a 95% confidence interval for ?

3) A college admissions director wishes to estimate the mean age of all students currently enrolled. In a random sample of 20 students, the mean age is found to be 22.9 years. From past studies, the standard deviation is known to be 1.5 years, and the population is normally distributed.

a. Construct a 90% confidence interval of the population mean age.

4) The weight of a product is measured in pounds. A sample of 50 units is taken from a batch. The sample yielded the following results: = 75 lbs., and σ = 10 lbs.

a. Calculate a 99% confidence interval for .

Answer 1

solution:1

sample size = n = 40

sample mean = = 29.6

population standard deviation = = 7.9

confidence level = CL = 95% = 0.95

since population standard deviation is known so z distribution is used

critical value of z =

margin of error (E) =

so margin of error for mean number of hour worked = 2.45

2)

sample size = n = 265

sample mean = = 63.8

population standard deviation = = 3.08

confidence level = CL = 95% = 0.95

since population standard deviation is known so z distribution is used

critical value of z =

margin of error (E) =

confidence interval =

lower limit of confidence interval = 63.08 - 0.37 = 62.71

upper limit = 63.08 + 0.37 = 63.45

so confidence interval is (62.71, 63.45)

3)

sample size = n = 20

sample mean = = 22.9

population standard deviation = = 1.5

confidence level = CL = 90% = 0.90

since population standard deviation is known and it is given that the distribution is normal.

critical value of z =

margin of error (E) =

confidence interval =

upper limit = 22.9 + 0.55 = 23.45

lower limit = 22.9 - 0.55 = 22.35

confidence interval is (22.35 , 23.45)

4)

sample size = n = 50

sample mean = = 75

population standard deviation = = 10

confidence level = CL = 99% = 0.99

since population standard deviation is known

critical value of z =

margin of error (E) =

confidence interval =

upper limit = 75+3.64 = 78.64

lower limit = 75-3.64 = 71.36

confidence interval is (71.36, 78.64)