Question

For a ??? ???h?, a 3/8 ?? drill should be turning at 1066 ??? when drilling mild steel. ????? readings of the turning speed of the drill were taken: 1065, 1079, 1083, 1063, 1058, 1076, 1050. You need to test if the true turning speed is equal or different from the specified turning speed of 1066 ???.

a. Write down the ???? and ??????????? hypotheses to be tested.

b.What type of statistical test procedure you will choose to test the hypotheses written above? Explain.

c.Construct a 95% Confidence Interval for the true mean turning speed. Test the hypotheses using the Confidence Interval constructed. Clearly interpret the test result.

d. Test the hypotheses using the test statistic method. Do you get the same answer as part (c)?

e. What is the ? ????? of the test? Test the hypotheses using the ? ?????. Do you get the same answer as parts (c) and (d)?

Answer 1

A)

Ho :   µ =   1066
Ha :   µ ╪   1066
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b)

1 mean hypothesis test will be used

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c)

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   12.0238
Sample Size ,   n =    7
Sample Mean,    x̅ = ΣX/n =    1067.7143
Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   6          
't value='   tα/2=   2.4469   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   12.0238   / √   7   =   8.148900
margin of error , E=t*SE =   2.4469   *   8.14890   =   19.939640
                  
confidence interval is                   
Interval Lower Limit = x̅ - E =    1067.71   -   19.939640   =   1047.775
Interval Upper Limit = x̅ + E =    1067.71   -   19.939640   =   1087.654
95%   confidence interval is (   1047.77   < µ <   1087.65   )

1066 lie with in the CI ,so do not reject Ho
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d)

degree of freedom=   DF=n-1=   6                  
                          
Standard Error , SE = s/√n =   12.0238   / √    7   =   8.1489      
t-test statistic= (x̅ - µ )/SE = (   1067.714   -   1066   ) /    8.1489   =   0.21
                          
critical t value, t* =    ±   2.4469   [Excel formula =t.inv(α/no. of tails,df) ]      

decision : test stat < critical value , do not reject Ho

same result as part c
                          

e)

p-Value   =   0.8403   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value>α, Do not reject null hypothesis

same result as part c and d

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Please revert back in case of any doubt.

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