Tests of means and proportions help please.?

Question

I need major help with this problem and one know how to solve it.

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?

Answer 1

ANSWER: "true mean" of fax transmissions are to a 0.01 level of significance greater than 10 pages.

SINGLE SAMPLE TEST, ONE-TAILED, 7 - Step Procedure for t Distributions, "one-tailed test"

1. Parameter of interest: "μ" = population mean  fax transmission number of pages

2. Null hypothesis Ho: μ = 10

3. Alternative hypothesis Ha: μ > 10

4. Test statistic formula: t = (x-bar - μ)/(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]

μ = 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 α = 0.01 the above shows P-value <= α, [0.0000006 <= 0.01]. Null hypothesis Ho: μ =  10 should be rejected. Fax transmissions are to a 0.01 level of significance greater than 10 pages.