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.

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

To answer this question, we will perform a hypothesis test and calculate the p-value using the given sample mean, standard deviation, and significance level.

(a) Hypothesis Test:
The null hypothesis (H0) is that the true mean is equal to 10 pages.
The alternative hypothesis (H1) is that the true mean is greater than 10 pages.

Step 1: Set up the hypotheses:
H0: μ = 10 (Null hypothesis)
H1: μ > 10 (Alternative hypothesis)

Step 2: Determine the test statistic:
Since we have a sample mean and standard deviation, we will use the t-distribution.
The test statistic formula is: t = (sample mean - hypothesized mean) / (standard deviation / sqrt(n))
Where n is the sample size.

Step 3: Set the significance level (α):
The significance level, in this case, is given as α = 0.01.

Step 4: Calculate the test statistic:
t = (14.44 - 10) / (4.45 / sqrt(35))

Step 5: Determine the critical value:
Since this is a one-tailed test (looking for the true mean to be greater), we need to find the critical value with α = 0.01 and (n-1) degrees of freedom (where n is the sample size). We'll use a t-distribution table or a calculator to find this value.

Step 6: Compare the test statistic with the critical value:
If the test statistic is greater than the critical value, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

(b) P-value Calculation using Excel:
To find the right-tail p-value using Excel, we will use the T.DIST.RT function.

The formula to calculate the p-value is: p-value = 1 - T.DIST.RT(t, n-1)

Where t is the test statistic and n is the sample size.

Now, let's calculate the test statistic and the p-value using the given data.