Question 4 (answer all please)

4. Alpha level and the critical region When a researcher sets a = .05, she is willing to accept a probability or less that she rejects the null hypothesis when it is actually true. Use the following Distributions tool to identify the boundaries that separate the extreme samples from the samples that are more obviously consistent with the null hypothesis. Assume the null hypothesis is nondirectional, meaning that the critical region is split across both tails of the distribution. The z-score boundaries at an alpha level a = .05 are: z = 3.29 and z = -3.29 Oz = 1.96 and z = -1.96 Oz = 2.58 and z = -2.58 To use the tool to identify the z-score boundaries, click on the icon with two orange lines, and slide the orange lines until the area in the critical region equals the alpha level. Remember that the probability will need to be split between the two tails. To use the tool to help you evaluate the hypothesis, click on the icon with the purple line, place the two orange lines on the critical values, and then place the purple line on the z statistic. Standard Normal Distribution Mean = 0.0 Standard Deviation = 1.0 5000 2500 -2500 O - 1 -0.67 0.67 The critical region is The z-score boundaries for an alpha level a = 0.001 are: Oz = 3.29 and z = -3.29 oz = 1.96 and z = -1.96 oz = 2.58 and z = -2.58 Suppose that the calculated z statistic for a particular hypothesis test is 4.16 and the alpha is 0.001. This z statistic is_ the critical region. Therefore, the researcher_ reject the null hypothesis, and she conclude the alternative hypothesis is probably correct