A certain manufactured product is supposed to contain 22% potassium by weight. A

Question

A certain manufactured product is supposed to contain 22% potassium by weight. A sample of 10 specimens of this product had an average of 22.56 and and a standard deviation of s = 0.42. If the mean percentage is found to differ from 22, the manufacturing process will be recalibrated. Using alpha = 0.05, test an appropriate null and alternate hypotheses. (a) the degree of freedom (b) the critical t value (c) the test statistic The final conclusion is A. We can reject the null hypothesis that mu = 22. B. There is not sufficient evidence to reject the null hypothesis that mu = 22.

Explanation / Answer

A)

As n = 10,

df = n - 1 = 9 [ANSWER]

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b)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   22  
Ha:    u   =/   22  
              
As we can see, this is a    two   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    9          

Hence, by table, at 0.05 level,

tcrit = -2.262, 2.262   [ANSWER]  

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c)
              
Getting the test statistic, as              
              
X = sample mean =    22.56          
uo = hypothesized mean =    22          
n = sample size =    10          
s = standard deviation =    0.42          
              
Thus, t = (X - uo) * sqrt(n) / s =    4.216370214 [ANSWER]

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d)

As |t| > 2.262, we reject Ho.

[ANSWER, OPTION A]

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