Measurements on the percentage of enrichment of 12 fuel rods

Measurements on the percentage of enrichment of 12 fuel rods used in a nuclear reactor were reported as follows; Test the Hypothesis H_0: mu = 2.95 versus H_1: mu_0 2.95, and draw appropriate conclusions. Use the P-value approach. Find a 99% two-sided Cl on the mean percentage of enrichment. Are you comfortable with the statement that the mean percentage of enrichment is 2.95%? Why? c. What would you use to check the normality assumption of the data?

Solution

A)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   2.95  
Ha:    u   =/   2.95  
              
As we can see, this is a    two   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    2.997272727          
uo = hypothesized mean =    2.95          
n = sample size =    11          
s = standard deviation =    0.110008264          
              
Thus, t = (X - uo) * sqrt(n) / s =    1.425219281          
              
Also, the p value is, as df = n - 1 = 11,              
              
p =    0.184550102          
              
As P > 0.01, we   FAIL TO REJECT THE NULL HYPOTHESIS.  

Thus, there is no significant evidence that the mean percentage of enrichment is not 2.95. [CONCLUSION]

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B)

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.005          
X = sample mean =    2.997777778          
t(alpha/2) = critical t for the confidence interval =    3.355387331          
s = sample standard deviation =    0.108717268          
n = sample size =    9          
df = n - 1 =    8          
Thus,              
              
Lower bound =    2.876181596          
Upper bound =    3.119373959          
              
Thus, the confidence interval is              
              
(   2.876181596   ,   3.119373959   )

As 2.95 is within this interval, then yes, it is okay. [ANSWER]

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c)

We can use a normal distribution plot and see if it is linear.