Question

Question 1

The mean starting salary of job with certain degree is unknown. Based on a sample of starting salary of 25 employees, the mean salary turns out to be $45,750/year. Assume that the population of all starting salaries follows a normal distribution with standard deviation $9125.

To find a 95% confidence interval estimate of mean staring salary, what interval estimate will you use?

Group of answer choices

T-interval

Z-interval

Question 2

The mean starting salary of job with certain degree is unknown. Based on a sample of starting salary of 25 employees, the mean salary turns out to be $45,750/year. Assume that the population of all starting salaries follows a normal distribution with standard deviation $9125.

Find a 95% confidence interval estimate of mean staring salary.

Group of answer choices

(42748, 48752)

(42173, 49327)

(41659,49841)

Question 3

The average speed of all cars passing though a certain road is unknown. The following data refers to the speed, measured in miles/hour, for a sample of 9 cars passing through the road on a given day.

49

52

57

45

55

47

44

43

39

We wish to find a 95% confidence interval of mean speed of all cars passing through the road.

What confidence interval will be appropriate for this problem?

Group of answer choices

T-interval

Z-interval

Question 4

The average speed of all cars passing though a certain road is unknown. The following data refers to the speed, measured in miles/hour, for a sample of 9 cars passing through the road on a given day.

49

52

57

45

55

47

44

43

39

Find a 95% confidence interval of mean speed of all cars passing through the road.

Group of answer choices

(42.47, 53.30)

(43.35, 52.43)

(44,23, 51.55)

Answer 1

1)

z interval

2)

sample mean, xbar = 45750
sample standard deviation, σ = 9125
sample size, n = 25

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, Zc = Z(α/2) = 1.96

ME = zc * σ/sqrt(n)
ME = 1.96 * 9125/sqrt(25)
ME = 3577

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (45750 - 1.96 * 9125/sqrt(25) , 45750 + 1.96 * 9125/sqrt(25))
CI = (42173 , 49327)

3)

t interval

4)
sample mean, xbar = 47.8889
sample standard deviation, s = 5.9043
sample size, n = 9
degrees of freedom, df = n - 1 = 8

Given CI level is 95%, hence α = 1 - 0.95 = 0.05
α/2 = 0.05/2 = 0.025, tc = t(α/2, df) = 2.306

ME = tc * s/sqrt(n)
ME = 2.306 * 5.9043/sqrt(9)
ME = 4.538

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (47.8889 - 2.306 * 5.9043/sqrt(9) , 47.8889 + 2.306 * 5.9043/sqrt(9))
CI = (43.35 , 52.43)