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

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 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages. (a) At the .01 level of significance, is the true mean greater than 10? (b) Use Excel to find the right-tail At the .01 level of significance, is the true mean greater than 10? ?
(a) ANSWER: Yes! The ';true mean'; of fax transmissions to a 0.01 level of significance are greater than 10 pages.





(b) ANSWER: Excel =TDIST(5.9,34,1) which is [5.80638E-07] the value in the ';right-tail';








Why??





SINGLE SAMPLE TEST, ONE-TAILED, 7 - Step Procedure for t Distributions, ';one-tailed test';





1. Parameter of interest: ';渭'; = population mean fax transmission number of pages





2. Null hypothesis Ho: 渭 = 10





3. Alternative hypothesis Ha: 渭 %26gt; 10





4. Test statistic formula: t = (x-bar - 渭)/(s/SQRT(n))


x-bar = estimate of the Population Mean (statistical mean of the sample) [14.44]


n = number of individuals in the sample [35]


s = sample standard deviation [4.45]


渭 = Population Mean [10] (used for Test statistic)





5. Computation of Test statistic formula t = 5.90





6. Determination of the P-value: The test is based on n -1 = 34 df (degrees of freedom). Table ';look-up'; value shows area under the 34 df curve to the right of t = 5.9 is (approximately) 0.0000006





7. Conclusion: with significance value 伪 = 0.01 the above shows P-value %26lt;= 伪, [0.0000006 %26lt;= 0.01]. Null hypothesis Ho: 渭 = 10 should be rejected. Fax transmissions are to a 0.01 level of significance greater than 10 pages.