Question

The company you work for, Capital Capacitors, makes a specialized capacitor. Data from six different production months has been collected:

January: 58,000 produced February: 71,000 produced March: 72,000 produced

April: 50,000 produced May: 54,000 produced June: 63,000 produced

The cost to produce one of these capacitors has been estimated to be $1.20.

1. What are the upper and lower bounds of a 95% confidence interval on the mean number of capacitors produced per month?

2. At an interest rate of 1% per month, what is the projected yearly cost, low and high estimates? Use your lower and upper bounds from 1. in your computations.

Answer 1

1)

Level of Significance ,    α =    0.01          
degree of freedom=   DF=n-1=   5          
't value='   tα/2=   4.0321   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   8981.4624   / √   6   =   3666.666667
margin of error , E=t*SE =   4.0321   *   3666.66667   =   14784.524273
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    61333.33   -   14784.524273   =   46548.809060
Interval Upper Limit = x̅ + E =    61333.33   -   14784.524273   =   76117.857606
99%   confidence interval is (   46549 < µ <   76118 )

2)

Low =46549 * 1.2 = 55858.8

After ineterst rate = 55858.8 *1.12 = 62562( Not compounded)

High =76118 * 1.2 = 91341.6

After ineterst rate = 91341.6*1.12 = 102303( Not compounded)

Please note that we have assume 99% cofidence level and interest rate not compounede.

Please revert back in case of any doubt.

Please upvote. Thanks in advance.