Please provide stepsSolution3 a Formulating the null and alt

Solution

3.

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   50  
Ha:    u   >   50   [ANSWER]

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b)

We assume that the population is approximately normally distirbuted.
              
As we can see, this is a    right   tailed test.      
              
Thus, getting the critical t,              
df = n - 1 =    15          
tcrit =    +   1.340605608      
              
Getting the test statistic, as              
              
X = sample mean =    52.7          
uo = hypothesized mean =    50          
n = sample size =    16          
s = standard deviation =    4.8          
              
Thus, t = (X - uo) * sqrt(n) / s =    2.25      
As t > 1.3406, we Reject Ho.

Thus, there is significant evidence that the population mean penetration exceeds 50 mils at 0.1 level. [CONCLUSION]

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c)
              
i)

Also, the p value is, using a table,              
0.01 < P < 0.025 [ANSWER]

ii)

Using technology, we find the exact value of P,
              
p =    0.019944003   [ANSWER]