Find the mean and the standard deviation Round intermediate

Find the mean and the standard deviation. (Round intermediate calculations to 4 decimal places. Round your answers to 2 decimal places.)

Calculate the value of the test statistic. (Round intermediate calculations to 4 decimal places. Round your answer to 2 decimal places.)

Approximate the p-value of the test statistic.

Solution

a)

Using technology,

X = sample mean =    21.28571429   [ANSWER]      

s = standard deviation =    2.36038737 [ANSWER]

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B)

Formulating the null and alternative hypotheses,              
              
Ho:   u   =   19  
Ha:    u   =/   19  
              
As we can see, this is a    two   tailed test.      
              
df = n - 1 =    6          
              
Getting the test statistic, as              
              
X = sample mean =    21.28571429          
uo = hypothesized mean =    19          
n = sample size =    7          
s = standard deviation =    2.360387377          
              
Thus, t = (X - uo) * sqrt(n) / s =    2.562050461 [ANSWER, TEST STATISTIC]

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C)
              
Also, the p value is, using a table, with df = 6,              
              
0.02 < P < 0.05   [ANSWER]

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d)

Reject Ho since the P value is LESS THAN alpha. [ANSWER]