Step by Step Example of Hypothesis Testing of a Proportion

The Scenario O In a Gallup Poll conducted in September, 1996, 33% of adult Americans believed in haunted houses. O In a Gallup Poll conducted June 6-8, 2005, 370 of 1002 adult Americans aged 18 or older believed in haunted houses. O Is there significant evidence to support the claim that the proportion of adult Americans who believe in haunted houses is not 33% at level of significance level of 0.05?

Step 1: Find the values of np and nq. O n is the sample size… O 1002 O p is the population parameter… O 33% or 0.33 O q is the complement (1-p)… O 67% or 0.67 O So np = O nq = O Both are ≥ 5, so we can continue

Step 2: Identify Claim, Null & Alternative Hypotheses O Claim: The proportion of adults who believe in haunted houses is not 33% O Null Hypothesis: Ho: x = 0.33 O Alternative Hypothesis: Ha: x ≠ 0.33 O The claim is the Alternative Hypothesis.

Step 3: Specify the Level of Significance O According to the original problem, the level of significance will be 0.05.

Step 4: Make a Normal Curve O Mark a normal curve off from -3 to +3, ready to use.

Step 5: Determine any Critical Values 3. What type of “tailed” graph will this be… 1. What was the significance value? What was the inequality sign for the Alternative Hypothesis? ≠ Two tailed, which means the critical values will be ±1.96

Step 6: Determine the Rejection Region(s) O Shade the region where it is improbable for the answer to be true (this will be where the null hypothesis is rejected). O Shade the area to the right of 1.96 and left of

Step 7: Calculate the Z-Score O Remember, p = 0.33, q=0.67 and n=1002. O If 370 of 1002 believe in haunted houses in the sample, what is p- hat? O P-hat = 0.37

And the answer is… Z = 2.69

Step 8: Do you Reject the Null Hypothesis? O Because the value of z is in the shaded area, the Null Hypothesis (Ho) will be rejected.

Step 9: Put into Context of Original Problem O There is enough evidence to support the claim that the proportion of adult Americans who believe in haunted houses is not 33%. O So is it higher, or lower??? We Exist!!!

Can we come to your house???