Question

Faced with rising fax costs, a firm issued a guideline that transmissions of 9 pages or more should be sent by 2-day mail instead. Exceptions are allowed, but they want the average to be 9 or below. The firm examined 25 randomly chosen fax transmissions during the next year, yielding a sample mean of 10.84 with a standard deviation of 3.07 pages.

(a-1) Find the test statistic. (Round your answer to 4 decimal places.) The test statistic 2.441

(a-2) At the .01 level of significance, is the true mean greater than 9? Yes No

(b) Use Excel to find the right-tail p-value. (Round your answer to 4 decimal places.) p-value

Answer 1

H0: 9

Ha: < 9

a)

Test statistics

t = ( - ) / ( S / sqrt(n) )

= ( 10.84 - 9) / ( 3.07 / sqrt(25))

= 2.9967

b)

df = n - 1 = 25 - 1 = 24

From T table,

t critical value at 0.05 level with 24 df = 1.711

Since t > 1.711 , Reject H0. Yes

c)

P(t > 2.9967) = T.DIST.RT ( x , deg_freedom) [ Using EXCEL ]

= T.DIST.RT ( 2.9967 , 24)

= 0.0031