Advanced Data Analysis – Hypothesis Testing Hypothesis Tests  z-test Used to test hypotheses that a mean is greater (less) than or equal to some value For example -- Do ISU students, on average, run 3 miles per day? Marketing 444 students conducted a simple random sample on campus, n=100

Advanced Data Analysis – Hypothesis Testing Steps in Hypothesis Testing  State Null and alternative hypotheses (Null always means no relationship – reject it if you can) Ho:  = 3 Ha:  ≠ 3  Specify the level of statistical significance (  ) This is 1 - Confidence Interval Most often.05 (in Marketing Research)  Specify the critical region to be used Areas of rejection (of Ho) and cannot reject (of Ho)

Advanced Data Analysis – Hypothesis Testing Collect data and determine test statistic  For example n = 100 (with SRS) mean = 3.2 s = 1.0 Test hypothesis -- reject or retain the null hypothesis  Compute z Where z = computed mean –  s x  computed z ≥ 1.96

Advanced Data Analysis – Hypothesis Testing What if: n = 100 (with SRS) Mean = 3.4 s = 4.0 n = 500 Mean = 3.4 s = 4.0 Importance of n and s

Advanced Data Analysis – Hypothesis Testing Laczniak Yogurt Company is interested in determining and comparing customer’s attitudes toward its main product in the southern versus northern region of the country. To make this determination, data were gathered from 81 customers in the south and 125 customers in the north. The hypothesis is that attitudes among northern customers are more favorable, because Laczniak Co. is located in New London, WI, and typically sponsors activities in the northern tier of states.

Advanced Data Analysis – Hypothesis Testing  The following data were obtained on a 1 (bad) to 7 (excellent) scale:  South M2 = 4.64 s2 = 3.00  North M1 = 5.20 s1 = 2.50  State Null and alternative hypotheses (Null always means no relationship – reject it if you can) Ho:    Ha:  >  Compute Z Test  |Z| ≥ 1.96

Advanced Data Analysis – Hypothesis Testing What if sample size in both were 144? What if s in both = 1.00?