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-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 10

Answer 1

Explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ ≤ 10

For the alternative hypothesis,

µ > 10

The inequality sign indicates that It is a right tailed.

Since the population standard deviation is not given, the distribution is a student's t.

Since n = 35,

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

t = (x - µ)/(s/√n)

Where

x = sample mean = 14.44

µ = population mean = 10

s = samples standard deviation = 4.45

t = (14.44 - 10)/(4.45/√35) = 5.9

We would determine the p value using the t test calculator. It becomes

p < 0.00001

Since alpha, 0.01 > than the p value, then we would reject the null hypothesis. Therefore, At a 1% level of significance, we can conclude that the true mean is greater than 10.