# statistics

Show ALL of your work if the problem requires it.

PART 1

#1

If you use a 95% confidence level in a two-tail hypothesis test, what will you decide about your Null Hypothesis if the computed value of the test statistic is Z = 2.57? Why?

#2.

You are the manager of a restaurant for a fast-food franchise. Last month, the mean waiting time at the drive- through window for branches in your geographical region, as measured from the time a customer places an order until the time the customer receives the order, was 3.7 minutes. You select a random sample of 64 orders. The sample mean waiting time is 3.57 minutes, with a sample standard deviation of 0.8 minute.

a)         At a 95% confidence level, is there evidence that the population mean waiting time is different from 3.7 minutes?

b)         Because the sample size is 64, do you need to be concerned about the shape of the population distribution when conducting the t- test in (a)? Explain.

PART 2

For this week you will need to read sections  9.1 and 9.2 in your textbook and go over the lecture notes.  Watch the following videos as a supplement

9.1 Hypothesis Testing with a known standard deviation

9.2 Hypothesis testing with an unknown standard deviation ( t-test)

The problems below are from Chapter 9.  #1 is from 9.1 and 9.2.  You will use the Critical Value Approach to Hypothesis Testing ( both the Z test and t test).

#1.       CHAPTER 9: HYPOTHESIS TESTING

an example problem

A manufacturer of chocolate candies uses machines to package candies as they move along a filling line. Although the packages are labeled as 8 ounces, the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces. A sample of 50 packages is selected periodically, and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces. Suppose that in a particular sample of 50 packages, the mean amount dispensed is 8.159 ounces, with a population standard deviation of 0.051 ounce.

Is there evidence that the population mean amount is different from 8.17 ounces? (Use a 95% confidence level).

a. State the variables and their assigned value according to the problem ( X (Sample Mean), μ (population mean), n (sample size), σ ( Standard deviation)

b. According to the information, state the Null and the Alternative Hypothesis.

c. State the level of significance, α according to the problem

d. What is the appropriate test and why?

e. Determine the critical Values according to the α value in part c

f. Compute the value of the test statistic ( Hint since we are in chapter 9, you will be using the Z test for the mean with a known standard deviation)

g.  Make a statistical decision, determine whether the assumptions are valid, and the managerial conclusion in the context of the theory, claim, or assertion being tested.  If the test statistic fall into the nonrejection region, you do not reject the null hypothesis.  If the test statistic falls into the rejection region, you reject the null hypothesis.

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