Presentation on theme: "Hypothesis Test II: t tests"— Presentation transcript:
1Hypothesis Test II: t tests Test for one population meanTest for the difference of two population means
2Hypothesis Tests for Population Parameters Population proportionPopulation meanDifference between two population means
35 Steps in Hypothesis Tests Step 1. Determine the null (Ho) and alternative (Ha) hypothesesHo : the population parameter = a constant (called the null value)Ha : upper or lower or two-tailed
45 Steps in Hypothesis Tests Step 2. Find an appropriate test statistic and pre-set the level of significance (called a level)Test statistic =(Sample estimate – null value)(S.E. of sample null value)a= 0.05 (or 0.01 or 0.10)
55 Steps in Hypothesis Tests Step 3. Check the conditions and find the p-value assuming Ho is trueThe calculation of the p-value depends on theHa.
65 Steps in Hypothesis Tests Step 4. Decide whether or not reject Ho based on the p-valuep-value > a fail to reject Hop-value < a reject Ho (= accept Ha)
75 Steps in Hypothesis Tests Step 5. Report the result in the context of the situationReject Ho There is sufficient evidence to support (Ha).Fail to reject Ho There is not sufficient evidence to support (Ha).
8Hypothesis Test for a Population Mean Step 1. Ho: m = moThree possible Ha’s:Ha: m = mo (two-tailed)orHa: m < mo (lower-tailed)Ha: m > mo (upper-tailed)
9Hypothesis Test for a Population Mean Step 2. test statistic
10Hypothesis Test for a Population Mean Step 3:Condition: Must be a random sample and the data must be bell-shaped (or normal)When the above conditions are met, use t-Table to find p-value (the required df = n-1)This test is called “one-sample t-test.”
11ExamplesThe average cost of 30 randomly selected used cars in a used car lot was $5,000 with sample standard deviation of $1,000.Find the p-value for testingHo: m = $4,500 vs. Ha: m = $4,500.Answer: t = 2.74 and < p-value < 0.016
12Examples Find the p-value for testing Ho: m = $4,500 vs. Ha: m > $4,500.Ho: m = $4,500 vs. Ha: m < $4,500.
14Hypothesis Test for the Difference of Two Population Means Step 1. Ho: m1 = m2Three possible Ha’s:Ha: m1 = m2 (two-tailed)orHa: m1 < m2 (lower-tailed)Ha: m1 > m2 (upper-tailed)
15Hypothesis Test for the Difference between Two Population Means Step 2. test statistic
16Hypothesis Test for the Difference between Two Population Means Step 3:Must be two independent random samples; the both samples must be bell-shaped (or normal)When the above conditions are met, use t-Table to find the p-value (the required df is the smaller one of (n1-1) and (n2-1))This test is called “Two-sample t-test.”
17ExamplesThe average waiting time for 50 students to connect to the college server from the dormitories was 5 seconds, while the average time to connect for 20 students living off-campus apartments was 10 seconds. Assume the times to connect in the dormitories and the apartments are both bell-shaped. The sample standard deviations were 2 seconds for dormitories and 8 seconds for apartments
18Examples Find the p-value for testing Ho: m1 = m2 vs. Ha: m1 = m2 Answer: t = -2.761: dormitories; 2: apartments