Hypothesis Testing: Mean & Population proportion

See attachment for complete problems.

Week 1: Quiz: Hypothesis Testing & One sample tests
Due on March 8, 2010 in your Individual Forum

Directions: For the following one-sample tests, identify the null and alternative hypothesis, and the critical value. Then, calculate the test statistic, note the p value and make a decision on the null hypothesis. Please show your work if you calculated manually. If you used statistical software, please show output. Your p value will be approximate if you use manual calculation (i.e., less than .05) or exact (if you used statistical software).

1: Hypothesis test for the population mean: t test (.5 point)
An electronics manufacturing process has a scheduled mean completion time of minutes. It is claimed that, under new management, the mean completion time, , is less than minutes. To test this claim, a random sample of completion times under new management was taken.
The sample had a mean completion time of minutes and a standard deviation of minutes. Assume that the population of completion times under new management is normally distributed. At the level of significance, can it be concluded that the mean completion time, , under new management is less than the scheduled mean?
Perform a one-tailed test.
Answers:

1: State the null & alternative hypothesis:
2: Identify critical value
3: Calculate test statistic
(p value)
4: State your decision on H0

2: Hypothesis test for a population proportion (.5 point)
The manufacturer of a new antidepressant claims that, among all people with depression who use the drug, the proportion of people who find relief from depression is at least . A random sample of patients who use this new drug is selected, and of them find relief from depression. Based on these data, can we reject the manufacturer's claim at the level of significance?
Perform a one-tailed test.
Answers:

1: State the null & alternative hypothesis:
2: Identify critical value
3: Calculate test statistic
(p value)
4: State your decision on H0

Directions: You may include the statistical software output, but you must also include a well-written explanation of the findings. Be sure to answer the question asked in each problem, and explain your decision with reference to your output. If you calculate the answers manually, be sure to show your work. I would prefer a Word document with your answers below each problem, but you may also submit an Excel document. Please submit only one document! Be sure to clearly state your decision on the null hypothesis

1: 9.54 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 55 randomly chosen fax transmissions during the next year, yielding a sample mean of 10.82 with a standard deviation of 1.95 pages. At the .05 level of significance, is the true mean greater than 10? Explain your decision.

2: 9.62 The Web-based company Oh Baby! Gifts have a goal of processing 95 percent of its orders on the same day they are received. If 122 out of the next 125 orders are processed on the same day, would this prove that they are exceeding their goal, using α = .05? Explain your decision.

3: 9.31: At Oxnard University, a sample of 18 senior accounting majors showed a mean cumulative GPA of 3.40 with a standard deviation of 0.20. At α = .05 in a two-tailed test, does this differ significantly from 3.25 (the mean GPA for all business school seniors at the university)? Explain.