SOLUTION: A company that sells mail order systems has been planning inventory and staffing based on an assumption that the mean of their weekly sales is 180. The weekly sales are normally di

Question 135343: A company that sells mail order systems has been planning inventory and staffing based on an assumption that the mean of their weekly sales is 180. The weekly sales are normally distributed. The company selects 10 weeks at random from the past year and obtains the data shown below.
Weekly sales:
179 172 170 179 194

189 176 198 193 178
Set up the hypothesis test to test weather the sample mean is different from 185
At the 0.05 significance, what can you conclude about the company's assumption?
Treat as a large sample.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A company that sells mail order systems has been planning inventory and staffing based on an assumption that the mean of their weekly sales is 180. The weekly sales are normally distributed. The company selects 10 weeks at random from the past year and obtains the data shown below.
Weekly sales:
179 172 170 179 194 189 176 198 193 178
Set up the hypothesis test to test weather the sample mean is different from 185
At the 0.05 significance, what can you conclude about the company's assumption?
Treat as a large sample.
--------------------------------
x-bar = 182.8 ; s = 9.87477..
--------------------------------
Ho: u=185
Ha: u Is not 185
----------------------
Critical value for 2-tail test with alpha = 5%: z= +/- 1.96
------------------------
Test statistic: z(182.8) = (182.8-185)/[9.87477/sqrt(10)] = -0.704523
-----------------------------------------
Conclusion: Since test statistic is not in the reject interval, Fail
to reject Ho. The test gives statistical evidence the u=185
===========================================
Cheers,
Stan H.

RELATED QUESTIONS
Based on the this problem, can you approximate a line of best fit by writing an equation? (answered by stanbon)

an electric store has a current inventory of 50 stereo systems. The lowest priced stereo... (answered by greenestamps)

My homework is needed tommorow and have no idea of working through it . please assist or (answered by uma)

It has been reported that 83% of federal government employees use e-mail. If a sample of... (answered by math_tutor2020)

a mail order company adds a shipping and handling fee of $4 for any order that weighs... (answered by jorel555,MathTherapy)

A family is relocating from St. Louis, Missouri, to California. Due to an increasing... (answered by Boreal)

you can order 3 shirts for 33 from a certain mail order company, from that same company... (answered by ikleyn)

the science company finds out that when it sells systems for $1200 each, they sell 70... (answered by Sarpi)