Bluman A.G. Elementary Statistics- A Step By Step Approach

Section 8–1 Steps in Hypothesis Testing—Traditional Method 409Similar procedures are used to find other values of a.Figure 8–9 with rejection regions shaded shows the critical value (C.V.) for the threesituations discussed in this section for values of a 0.10, a 0.05, and a 0.01. Theprocedure for finding critical values is outlined next (where k is a specified number).Figure 8–9Summary ofHypothesis Testingand Critical ValuesH 0 : = kH 1 : < k = 0.10, C.V. = –1.28 = 0.05, C.V. = –1.65 = 0.01, C.V. = –2.33(a) Left-tailed 0H 0 : = kH 1 : > k = 0.10, C.V. = +1.28 = 0.05, C.V. = +1.65 = 0.01, C.V. = +2.33(b) Right-tailed0H 0 : = kH 1 : ≠ k = 0.10, C.V. = ±1.65 = 0.05, C.V. = ±1.96 = 0.01, C.V. = ±2.58(c) Two-tailed 0Procedure TableFinding the Critical Values for Specific A Values, Using Table EStep 1Step 2Draw the figure and indicate the appropriate area.a. If the test is left-tailed, the critical region, with an area equal to a, will be on theleft side of the mean.b. If the test is right-tailed, the critical region, with an area equal to a, will be onthe right side of the mean.c. If the test is two-tailed, a must be divided by 2; one-half of the area will be tothe right of the mean, and one-half will be to the left of the mean.a. For a left-tailed test, use the z value that corresponds to the area equivalent to ain Table E.b. For a right-tailed test, use the z value that corresponds to the area equivalent to1 a.c. For a two-tailed test, use the z value that corresponds to a2 for the left value. Itwill be negative. For the right value, use the z value that corresponds to the areaequivalent to 1 a2. It will be positive.8–11