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Hypothesis Tests Steps and Notation (1-Sample) STEP 1, Null and Alternate Hypotheses State the “Null Hypothesis” H0 : and “Alternate Hypothesis” Ha : STEP 1, Null and Alternate Hypotheses The Null Hypothesis is what we assume. We will try to reject this assumption (i.e., reject the Null) with significant evidence. TIP: Always put an equal sign for the Null. Fill out the Null Hypothesis AFTER filling out the Alternate Hypothesis. H0 : STEP 1, Null and Alternate Hypotheses The Alternate Hypothesis is what we want to show. This comes from the question in the paragraph. In filling out the Alternate Hypothesis, we are limited to three different inequality signs to choose from: Less Than Greater Than Not Equal To Ha : NOTE: “a” for “alternate” STEP 1, Null and Alternate Hypotheses Both the Null and Alternate Hypotheses are statements about the POPULATION. Therefore, the symbols that you use will be either p population proportion Ho : p Ha : p STEP 1, Null and Alternate Hypotheses Both the Null and Alternate Hypotheses are statements about the POPULATION. Therefore, the symbols that you use will be either p population proportion or population mean H o : Ha : STEP 1, Null and Alternate Hypotheses While reading the question in the paragraph, you will choose the inequality for the Alternate Hypothesis which best represents what the question wants to show. Once an inequality sign is chosen, the entire hypothesis test takes on a nickname. These nicknames tell you which tail you shade in the bell-shaped curve in STEP 4. TIP: During STEP 4, remember to look back at the inequality in the Alternate Hypothesis for shading. Ha : “Left-tailed” Ha : “Right-tailed” Ha : “Two-tailed” STEP 1, Null and Alternate Hypotheses Recall that you will fill out the Alternate hypothesis first by reading the question in the paragraph and seeing what it is that you want to show. For example, if you want to show that “…the percentage of all college students that own a cell phone is less than 99%.” Ho : Ha : p 0.99 then fill out the Alternate Hypothesis as follows. STEP 1, Null and Alternate Hypotheses Recall that you will fill out the Alternate hypothesis first by reading the question in the paragraph and seeing what it is that you want to show. For example, if you want to show that “…the percentage of all college students that own a cell phone is less than 99%.” then fill out the Alternate Hypothesis as follows. Ho : p H a : p 0.99 STEP 1, Null and Alternate Hypotheses The comparison number that you put into the Alternate Hypothesis will then be copied into the Null Hypothesis. So we will assume that the percentage of all college students that own a cell phone is equal to 99% until STEP 5. During STEP 5 we hope to reject this assumption H 0 . TIP: The Alternate Hypothesis H a is not referenced again until STEP 6 (the conclusion). Ho : p H a : p 0.99 STEP 1, Null and Alternate Hypotheses Recall that you will fill out the Alternate hypothesis first by reading the question in the paragraph and seeing what it is that you want to show. For example, if you want to show that “…the average cover price for all comic books published in 2012 is greater than $2.” then fill out the Alternate Hypothesis as follows. Ho : Ha : 2 STEP 1, Null and Alternate Hypotheses Recall that you will fill out the Alternate hypothesis first by reading the question in the paragraph and seeing what it is that you want to show. For example, if you want to show that “…the average cover price for all comic books published in 2012 is greater than $2.” then fill out the Alternate Hypothesis as follows. Ho : Ha : 2 STEP 1, Null and Alternate Hypotheses The comparison number that you put into the Alternate Hypothesis will then be copied into the Null Hypothesis. So we will assume that the average cover price for all comic books is equal to $2 until STEP 5. During STEP 5 we hope to reject this assumption H 0 . TIP: The Alternate Hypothesis H a is not referenced again until STEP 6 (the conclusion). Ho : Ha : 2 STEP 2, Significance Level State your Level of Significance. This is the comfort level of what you would call a “rare event.” TIP: This is usually 1% or 5%. TIP: The Significance Level is not used again until Step 5 where we compare it against the Pvalue. STEP 3, Statistics State your statistics. These will be the numbers which describe your SAMPLE. Sample size and either n sample proportion p̂ or sample mean and sample standard deviation x Sx n p̂ STEP 3, Statistics State your statistics. These will be the numbers which describe your SAMPLE. Sample size and either n sample proportion p̂ or sample mean and sample standard deviation x Sx n x Sx STEP 4, Part 1, Test Statistic Step 4 is done in two parts, and each part is a calculation. Part 1: Calculate the TEST STATISTIC: z pˆ p0 p0 1 p0 n z-score for proportions or t-score for means t x 0 Sx n STEP 4, Part 1, Test Statistic Note that and p0 and 0 numbers come from the Null Hypothesis H . The 0 subzero in the notation is to remind you that you are assuming these values from the Null Hypothesis. z pˆ p0 p0 1 p0 n t x 0 Sx n STEP 4, Part 2, P-value Part 2: Use the Test Statistic to calculate the Pvalue (Probability value). The P-value will be the shaded area in the curve. TIP: Look back at the Alternate Hypothesis H a in STEP 1 to see where to shade (left-tailed, righttailed, or two-tailed). You will shade the area of the tail after where the Test Statistic is (and its mirror image if “TwoTailed”) as indicated from H a . STEP 5, To reject or not to reject the Null Hypothesis Now that you have calculated the P-value from STEP 4, compare it with the Level of Significance from STEP 2. If the P-value < α then the probability of your sample occurring is small. In other words, your sample is “rare”, or “statistically significant” enough to reject your Null Hypothesis H 0 . P - value STEP 5, To reject or not to reject the Null Hypothesis If the P-value > α then the probability of your sample occurring is more common. In other words, your sample is “NOT rare”, or “NOT statistically significant” enough to reject your Null Hypothesis H 0 . P - value STEP 6, The conclusion In STEP 6 you state your conclusion in real-life terms. If, from STEP 5, the P-value < α then there is significant evidence to conclude H a . In other words… P - value There is significant evidence to conclude (whatever the question in the paragraph wanted to show). STEP 6, The conclusion If, from STEP 5, the P-value > α then there is NOT significant evidence to conclude H a . In other words… P - value There is NOT significant evidence to conclude (whatever the question in the paragraph wanted to show). THE END