Transcript 9-5
9-5 Day 1 Testing Paired Differences (independent samples) What do you do if samples are independent? Comparing period 5 Calc average on the midterm and period 6 Calc average midterm? Get a random sample of seniors and compare GPAs of girls to GPA of boys… If the samples are independent then you compare mean differences using a new formula σ Known or Unknown H0 : μ1 μ2 0 μ1 μ2 HA : μ1 μ2 0 μ1 μ2 Left Tailed HA : μ1 μ2 0 μ1 μ2 Right Tailed HA : μ1 μ2 0 μ1 μ2 Customary… Two Tailed And the usuals… x1 and x2 should have normal distributions with mean μ1 and μ2. If both n1 and n2 are larger than 30, then the CLT assures you that the distributions of the xbars are normal. How do I do it? So glad you asked!! Using the same pattern 1. State null and alternate hypotheses 2. Compute your test statistic 3. Find the P-value that corresponds to the sample test statistic 4. Conclude 5. State your conclusion σ known x1 x 2 μ1 μ2 z 2 1 2 2 σ σ n1 n2 z x1 x 2 2 1 2 2 σ σ n1 n2 σ unknown x1 x 2 μ1 μ2 t 2 1 2 2 s s n1 n2 t x1 x 2 2 1 2 2 s s n1 n2 Example A random sample of n1=12 winter days in Denver gave a mean pollution index of 43. For Englewood (a suburb of Denver) a random sample of n2=14 winter days gave a sample pollution index of 36. Assume that pollution index is normally distributed, and previous studies show σ1= 21 and σ2 = 15. Does this information suggest that the mean population pollution index of Englewood is different from Denver in the winter? Use 1% level of significance. Example A random sample of n1 =16 communities in western Kansas gave an average rate of hay fever (per 1000, under 25 yrs of age) of 109.50 with a sample standard deviation of 15.41. A random sample of n2 =14 regions in western Kansas gave an average rate of hay fever (per 1000, over 50 yrs of age) of 99.36 with a sample standard deviation of 11.57. Assuming that the hay fever rate of each group is approximately normal, does the data suggest that the 50+ has a lower rate of hay fever? Use a 5% level of confidence.