3. Trufit manufactures and assembles computer desks for work station cubicles. T

Question

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____________________________________________

Explanation / Answer

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

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