Question

The alpha level that a researcher sets at the beginning of the experiment is the level to which he wishes to limit the probability of making the error of . 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 α = .05 are: z = 1.96 and z = –1.96 z = 2.58 and z = –2.58 z = 3.29 and z = –3.29 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. The critical region is . The z-score boundaries for an alpha level α = 0.01 are: z = 3.29 and z = –3.29 z = 1.96 and z = –1.96 z = 2.58 and z = –2.58 Suppose that the calculated z statistic for a particular hypothesis test is 2.00 and the alpha is 0.01. This z statistic is the critical region. Therefore, the researcher reject the null hypothesis, and he conclude the alternative hypothesis is probably correct.

Answer 1

Answer:

Step-by-step explanation:

Hello!

Under the standard normal distribution, you have a two-tailed hypothesis set.

A hypothesis test is two-tailed means that the rejection region is divided into two equal areas in the tails of the distribution.

Under the null hypothesis curve, the "no rejection region" is the area "1-α" and "α" represents the rejection region, in this case, it is divided into two equal "tails" with is α/2

Generally speaking, you have two critical values that determine the tails of the rejection regions:

Lower critical value: $Z_{\alpha/2 }$

Upper critical value: $Z_{1-\alpha /2}$

1)

If you have a two-tailed hypothesis test with a significance level α: 0.05

The significance level will be divided into the two tails α/2: 0.025 and the critical values are defined as:

$Z_{\alpha/2 }= Z_{0.025}= -1.965$

$Z_{1-\alpha /2}= Z_{0.975}= 1.965$

(See first attachment for curves)

2)

In this item the hypotheses are two-tailed but the significance level is α: 0.01

Then the significance level will be divided into the two tails: α/2: 0.005

$Z_{\alpha/2 }= Z_{0.005}= -2.586$

$Z_{1-\alpha /2}= Z_{0.995}= 2.586$

(See second attachment for curves)

I hope it helps!