Question

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 p-value.

Answer 1

a) The calculated value t = 5.903 > 2.572 at 0.01 level of significance

Null hypothesis is rejected at 0.01 level of significance

There is a true mean value is less than 10

b) p - value 0.00001

The p - value 0.00001 < 0.01

The result is significant at p<0.01

Explanation:

Step(i):-

Given mean of the population = 10

Sample size 'n'= 35

Mean of the sample x⁻ = 14.44

Standard deviation of the sample 's' = 4.45

Level of significance ∝ = 0.01

Step(ii):-

Null Hypothesis H₀ : μ >10

Alternative Hypothesis : H₁ : μ < 10

Test statistic

`t = (x^(-) -mean)/((S)/(√(n) ) )`

`t = (14.44-10)/((4.45)/(√(35) ) )`

t = 5.903

Degrees of freedom = n-1 = 35-1 = 34

tabulated value t₀.₀₁,₃₄ = 2.572

The calculated value t = 5.903 > 2.572 at 0.01 level of significance

Null hypothesis is rejected at 0.01 level of significance

There is a true mean value is less than 10

p- value :

p - value 0.00001

The p - value 0.00001 < 0.01

The result is significant at p<0.01