Question

Recently many companies have been experimenting with telecommuting, allowing employees to work at home on their computers. Among other things, telecommuting is supposed to reduce the number of sick days taken. Suppose that at one firm, it is known that over the past few years employees have taken a mean of 5.4 sick days. This year, the firm introduces telecommuting. Management chooses a simple random sample of 80 employees to follow in detail, and at the end of the year, these employees average 4.5 sick days with a standard deviation of 2.7 days.

a) Describe the population in the context of this problem
b) Describe the parameter u in the context of this problem.
c) Describe the sample in the context of this problem.
d) Describe the statistic in the context of this problem
e) The firm would like to know if there is evidence that the true mean number of sick days for all employees of the firm has decreased after telecommuting was introduced. State the hypotheses. Use ?-0.10.
f) Check the assumptions. If you don't know if an assumption is satisfied based on the information provided, then state "We must assume
g) Calculate the test statistic
h) Find the p-value.
i) Make a decision.
j) State the conclusion in terms of the problem.

Answer 1

A.) Population : All employees at a firm

B.) μ = 5.4

C.) Sample : 80 employees at a firm

D.) Sample mean, x bar = 4.5

Explanation:

From the question :

E.)

H0: μ ≥ 5.4

H1 : μ < 5.4

F.)

If Pvalue < α ; Reject H0

G.)

Test statistic :

(xbar - μ) ÷ (s/sqrt(n))

(4.5 - 5.4) ÷ (2.7/sqrt(80))

-0.9 ÷ 0.3018691

= - 2.98

H.)

Pvalue fro Zscore calculator, α = 0.10 = 0.002882

I.)

Decision :

0.002882 < 0.10

Since, Pvalue < α ; We reject the Null

J.)

We Can conclude that the true mean number of sick days for all employees of the firm has decreased after telecommuting was introduced