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 8 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 8 or below. The firm examined 39 randomly chosen fax transmissions during the next year, yielding a sample mean of 8.81 with a standard deviation of 2.51 pages. (a-1) Find the test statistic. (Round your answer to 4 decimal places.) The test statistic (a-2) At the .01 level of significance, is the true mean greater than 8? Yes No (b) Use Excel to find the right-tail p-value. (Round your answer to 4 decimal places.) p-value

Solution

H0: mu = 8

Ha: mu>8

One tailed hypothesis test.

The hypothetical mean is 8.0000
The actual mean is 8.8100
The difference between these two values is 0.8100
The   95% confidence interval of this difference:
From -0.0036 to 1.6236

t statistic = 2.0153
  df = 38
  standard error of difference = 0.402

p value =0.0254

p >alpha

Hence accept null hypothesis.

The difference between sample mean and population mean is not statistically significant.