OneSample Tests of Hypothesis Chapter Ten Mc GrawHillIrwin

One-Sample Tests of Hypothesis Chapter Ten Mc. Graw-Hill/Irwin © 2006 The Mc. Graw-Hill Companies, Inc. , All Rights Reserved.

What is a Hypothesis? A statement about the value of a population parameter. Example: The mean monthly income for a systems analyst is $5 K.

Hypothesis testing • Process used to determine if the hypothesis is a reasonable statement • The hypothesis is either accepted or rejected • Decision is based on sample data & probability theory 3 K (say) $5 K 7 K (say) Process involves taking a sample & calculating the sample mean. Then we look at how far the sample mean is from the hypothesized mean. If it is too far, we reject it; else, we accept it. Eg. If the mean salary of a sample of systems analysts is between 3 -7 K, accept hyp.

Hypothesis Testing – Formal Steps Null: Innocent Alternate: Guilty Error level you are willing to tolerate; eg. 5% Identify method to weigh the evidence If evidence is stronger than error level (eg. 95%) reject null hypothesis. Listen to lawyers on both sides & decide based on above criteria

Practice time! Do Self-Review 10 -1 Page 287 -8 (2 tails) -2. 56

Step One : State the null and alternate hypotheses Generally H 0 represents what is currently believed. H 1 represents a researcher’s claim. H 1 is accepted if H 0 is shown to be false H 0: m = 0 H 1: m = 0 Three possibilities H 0: The mean income of women financial planners is $65, 000, ie. μ = $65, 000. H 1: The mean income of. . is not equal to… ie. μ ≠ $65000. H 0: m < 0 H 1: m > 0 H 0: The mean income of women financial planners is ≤ $65, 000 H 1: The mean income of. . is > $65000. H 0: m > 0 H 1: m < 0 H 0: The mean income of women financial planners is ≥ $65, 000 H 1: The mean income of. . is < $65000. The null hypothesis always contains equality.

Step Two: Select a Level of Significance is the probability ( α ) of rejecting the null hypothesis when it is actually true. α = P (Reject H 0 | H 0 is true) = Type I error We are deciding upfront how much type 1 error we are willing to tolerate. H 0: The suspect is innocent. H 1: The suspect is guilty. If we set the Level of Significance (α) at 0. 05 (5%), it implies that we are willing to convict with only 95% of evidence pointing to guilt (ie. Even though the suspect is innocent). If we set the Level of Significance for the testing at 0. 01 (1%), it implies that we could mistakenly convict an innocent person only 1% of the time.

Two types of errors in hypothesis testing α = P (Reject H 0 | H 0 is true) = Type I error β = P (Accept H 0 | H 0 is false) = Type II error Null Hypothesis Ho is true Ho is false Researcher Accepts Rejects Ho Ho Correct decision Type I error (a) Type II Error (b) Correct decision

Step 3: Identify test statistic Decide if you want to use z or t as the statistic. (No need to calculate anything yet!)

Step Four: Formulate the decision rule. Find the Critical Value(s) corresponding to α from the z or t table. Mark the rejection/ acceptance regions. H 0: m = 0 H 1: m = 0 2 tails testing H 0: m < 0 H 1: m > 0 1 tail testing

Step Five: Make a decision. • Now, you compute the z or t statistic. • Check if it falls inside the Rejection or Acceptance region • If it falls inside the Rejection region, reject H 0. • If it falls inside the Acceptance region, do not reject H 0.

p-Value The probability of observing a sample value as extreme as, or more extreme than the calculated test statistic value. p-value Cut-off Calculated Z Z Decision Rule: If the p-Value is smaller than the significance level, a, H 0 is rejected.

Practice Self-Review 10 -2, Page 291 (1 tail) (1 tail on the right) (from table for α=0. 01) 0. 01 Z=1. 81 Z=2. 33