Chapter 10 Basic Statistics Hypothesis Testing for Business and Economics Fifth Edition Chapter 10 Hypothesis Testing Douglas William Samuel Irwin/McGraw-Hill 1 1 1 2 1 1

Topics Covered ONE Define a hypothesis and hypothesis testing. TWO Describe the five step hypothesis testing procedure. THREE Distinguish between a one-tailed and a two-tailed test of hypothesis

Hypothesis What is Hypothesis ? A procedure based on sample evidence and probability theory to determine whether the hypothesis is a reasonable statement Example: “The mean monthly income for systems analysts is $6,325”.

Hypothesis What is Hypothesis Testing? Used to determine whether the hypothesis is a reasonable statement and should not be rejected, or is unreasonable and should be rejected. Based on sample evidence and probability theory.

Hypothesis 5 steps of testing hypothesis

Hypothesis Step One: State the null and alternate hypotheses Null Hypothesis H0, read “H sup zero” A statement about the value of a population parameter. Example; the null is that the mean number of miles driven on the steal-belted tire is not different from 60,000. The null hypothesis would be written H0:µ=60,000. Alternative Hypothesis H1, read “H sup 1” A statement that is accepted if the sample data provide evidence that the null hypothesis is false. Example; H1: µ = 60,000

Step One: State the null and alternate hypotheses H0: m = 0 H1: m = 0 Two tailed test One tailed test H0: m < 0 H1: m > 0

Hypothesis Step two: Select a level of significance Level of significance “α” Alpha ; the probability of rejecting the null hypothesis when it’s true ( Type Error I) or accepting the null hypothesis when it’s false (Type Error II). There is no level of significance that is applied to all tests. But usually we use .01 for quality assurance, .05 for consumer research projects.

Step three: Select the test statistic A value determined from sample information, used to determine whether to reject the null hypothesis. Examples: z, t, F, c2 z Distribution as a test statistic We refer to σ/√n as the Standard error of the mean

Step four: Formulate the decision rule The decision rule states the conditions when H0 is rejected. Critical value: The dividing point between the region where the null hypothesis is rejected and the region where it is not rejected.

Step four: Formulate the decision rule Sampling Distribution Of the Statistic z, a Right-Tailed Test, .05 Level of Significance

Step five: Make a decision The final step in hypothesis testing is computing the test statistic and comparing it to the critical value. When z = 2.34 The H0 rejected at .05 If z< 1.65 H0 is not rejected

Step 1 Step 4 Step 5 State the decision rule. Reject H0 if z > 1.96 or z < -1.96 or if p < .05. Step 5 Make a decision and interpret the results. Step 3 Identify the test statistic. Because we know the population standard deviation, the test statistic is z. Step 1 State the null and the alternative hypotheses H0: m = 16 H1: m = 16 Step 2 Select the significance level. The significance level is .05.

Exercises Example; 16 bottle of Cola been selected from a normal population with a mean of µ =31.2 ounces and a population standard deviation of σ=.4 ounces and find a sample mean to be X = 31.38 . To find the value of Z: z= 31.38-31.20 = 1.80 0.4/√16

Next we compute the likelihood of z value Greater than 1.80 . Appendix D, page 496 .0359 .4641 31.20 31.38 0 1.80 Z-value

As long as the sample size n > 30, z can be approximated using Testing for the Population Mean: Large Sample, Population Standard Deviation Unknown Testing for the Population Mean: Large Sample, Population Standard Deviation Unknown As long as the sample size n > 30, z can be approximated using Here s is unknown, so we estimate it with the sample standard deviation s.

Example of “ One Tail” Roder’s Discount Store chain issues its own credit card. Lisa, the credit manager, wants to find out if the mean monthly unpaid balance is more than $400. The level of significance is set at .05. A random check of 172 unpaid balances revealed the sample mean to be $407 and the sample standard deviation to be $38. Should Lisa conclude that the population mean is greater than $400, or is it reasonable to assume that the difference of $7 ($407-$400) is due to chance?

Make a decision and interpret the results. Step 4 H0 is rejected if z > 1.65 or if p < .05. Step 5 Make a decision and interpret the results. Step 3 Because the sample is large we can use the z distribution as the test statistic. Step 1 H0: µ < $400 H1: µ > $400 Step 2 The significance level is .05.

Make a decision and interpret the results. Step 5 Make a decision and interpret the results. Computed z of 2.42 > Critical z of 1.65, Reject H0 Lisa can conclude that the mean unpaid balance is greater than $400.

Exercises Page 291