Faced with rising fax costs a firm issued a guideline that t

Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below. The firm examined 20 randomly chosen fax transmissions during the next year, yielding a sample mean of 11.88 with a standard deviation of 5.37 pages.

Find the test statistic. (round to 4 decimal places)

At the .01 level of significance, is the true mean greater than 10?

Use Excel to find the right-tail p-value. (round to 4 decimal places)

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   10  
Ha:    u   >   10  
              
As we can see, this is a    right   tailed test.      
              
              
Getting the test statistic, as              
              
X = sample mean =    11.88          
uo = hypothesized mean =    10          
n = sample size =    20          
s = standard deviation =    5.37          
              
Thus, t = (X - uo) * sqrt(n) / s =    1.565663984 [ANSWER, TEST STATISTIC]

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Thus, getting the critical t,              
df = n - 1 =    19          
tcrit =    +   2.539483191      

As t < 2.539, we fail to rejct Ho.

The true mean is not greater than 10. [ANSWER]

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Also, the p value is, as df = 19,              
              
p =    0.066965412   [ANSWER]