I need help with the following questions and appreciate any and all help given.
1. Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by a 2-day mail instead. Exceptions are allowed, but they want the average to be 10 or below. The firm examined 35 randomly chosed 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.
Ho: µ ≤ 10 -->null hypothesis
Ha: µ > 10 -->alternative hypothesis
Using the z-test formula to find the test statistic:
z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)
z = (14.44 - 10)/(4.45/sqrt of 35)
I'll let you finish the calculation.
If the test statistic exceeds the critical value from the z-table at .01 level of significance for a one-tailed test (the alternative hypothesis shows a specific direction), the null will be rejected in favor of the alternative hypothesis and µ > 10.
The p-value is the actual level of the test statistic.
I hope this will get you started.
Thanks for all of your help.
Thanks for explaining the problem in terms that I can understand.
To answer these questions, we need to conduct a hypothesis test and calculate the p-value. Here are the steps to follow:
Step 1: State the hypotheses
- Null hypothesis (H0): The true mean number of pages is <= 10.
- Alternative hypothesis (H1): The true mean number of pages is > 10.
Step 2: Set the significance level
In this case, the significance level (alpha) is given as 0.01 (or 1%).
Step 3: Calculate the test statistic
The test statistic we will use is the t-statistic since the population standard deviation is unknown. The formula to calculate the t-statistic is:
t = (sample mean - hypothesized mean) / (sample standard deviation / √sample size)
In this case, we have:
sample mean (x̄) = 14.44
hypothesized mean (μ0) = 10
sample standard deviation (s) = 4.45
sample size (n) = 35
Calculating the t-statistic:
t = (14.44 - 10) / (4.45 / √35)
t ≈ 4.01 (rounded to two decimal places)
Step 4: Calculate the p-value
To find the right-tail p-value using Excel, we can use the T.DIST.RT function. The syntax of this function is T.DIST.RT(x, degrees_freedom), where x is the test statistic and degrees_freedom is the degrees of freedom (sample size - 1).
In this case, the formula in Excel would be:
=T.DIST.RT(4.01, 34)
Using Excel, the right-tail p-value is approximately 0.0001.
Step 5: Make a decision
(a) Since the alternative hypothesis is that the true mean is greater than 10, we will reject the null hypothesis if the p-value is less than the significance level (0.01).
The p-value (0.0001) is less than the significance level (0.01), so we reject the null hypothesis.
(b) The right-tail p-value is approximately 0.0001, as calculated in Excel.
To summarize:
(a) At the 0.01 level of significance, we reject the null hypothesis and conclude that the true mean number of pages is greater than 10.
(b) The right-tail p-value is approximately 0.0001 using Excel.