3 Trufit manufactures and assembles computer desks for work

3.            Trufit manufactures and assembles computer desks for work station cubicles. The weekly production of the Model VII desk at the Akron Plant follows the normal probability distribution with a mean of 400 desks and a standard deviation of 25 desks. Recently, a new lean production method was introduced and several experienced employees were given additional training. The VP of Operations would like to investigate whether there has been a change in the weekly production of the Model VII desk.   A sample from last year’s weekly production output (50 weeks) yielded a mean number of desks produced of 409.3 Test using 0.01 significance level.

Given in the problem:

n = 50

  = 409.3

= 25

a. What is the relevant formula when Testing for a Population Mean with a Known Population Standard Deviation?

Step 1: State the null hypothesis and the alternate hypothesis.

                                H₀: m

                                H₁: m

Step 2: Select the level of significance.

                                = 0.01 as stated in the problem.

Step 3: Select the test statistic.

Step 4: Formulate the decision rule.

                Reject H₀ if computed __ > critical + ____ of +_______ or computed ___ < critical –_____ of   – __________

Step 5: Compute the __________statistic, make a decision and interpret the result.

Decision: __________Null Hypothesis because____________________________________________

Solution

Set Up Hypothesis
Null Hypothesis H0: U=400
Alternate Hypothesis H1: U!=400
Test Statistic
Population Mean(U)=400
Given That X(Mean)=409.3
Standard Deviation(S.D)=25
Number (n)=50
we use Test Statistic (Z) = x-U/(s.d/Sqrt(n))
Zo=409.3-400/(25/Sqrt(50)
Zo =2.6304
| Zo | =2.6304
Critical Value
The Value of |Z | at LOS 0.01% is 2.58
We got |Zo| =2.6304 & | Z | =2.58
Make Decision
Hence Value of | Zo | > | Z | and Here we Reject Ho
P-Value : Two Tailed ( double the one tail ) - Ha : ( P != 2.6304 ) = 0.0085
Hence Value of P0.01 > 0.0085, Here we Reject Ho

ANS)
H0: U=400 , H1: U!=400
Reject H0 if computed Zo > critical 2.58 of or computed Zo < critical –2.58

Reject Ho