If the value given in the table for Z = z is k: that is, pr(Z > z) is 1 - k, then the two-tailed probability of observing a value which is at least as extreme, ie Pr(|Z| > z) is 0.5*(1-k).
The answer depends on whether the test is one-tailed or two-tailed.One-tailed: z = 1.28 Two-tailed: z = 1.64
For a two-tailed test at a 0.10 level of significance, you would divide the significance level by 2, giving 0.05 for each tail. The critical z-values corresponding to 0.05 in each tail are approximately ±1.645. Therefore, the critical values of z for this test are -1.645 and +1.645.
2.58
z = 1.56 gives a 2-tailed interval for 88%.z = 1.56 gives a 2-tailed interval for 88%.z = 1.56 gives a 2-tailed interval for 88%.z = 1.56 gives a 2-tailed interval for 88%.
Z = ± 1.8119 gives a two-tailed interval of 93%
The answer depends on whether the test is one-tailed or two-tailed.One-tailed: z = 1.28 Two-tailed: z = 1.64
-2.58,2.58
The critical value ( Z_a ) denotes the z-score that corresponds to a specified significance level ( a ) in a standard normal distribution. It is used in hypothesis testing to determine the threshold beyond which the null hypothesis is rejected. For example, in a one-tailed test, ( Z_a ) indicates the point at which the area under the curve to the right (or left, depending on the test) equals ( a ). In a two-tailed test, it helps define the critical regions in both tails of the distribution.
+2.58
For a two-tailed test at a 0.10 level of significance, you would divide the significance level by 2, giving 0.05 for each tail. The critical z-values corresponding to 0.05 in each tail are approximately ±1.645. Therefore, the critical values of z for this test are -1.645 and +1.645.
2.58
1.64
The type I error is 0.0027 only when a two tailed test is used with a z-score of ±3. There are many occasions when a one-tailed test is more appropriate and with the same test would have half the Type I error. Furthermore, it is more usual for the researcher to specify the type I error first - 0.05, 0.01 or 0.001 are favourites - and to select one-or two-tailed critical region after that. It is, therefore, more likely that the Type I error is a "round" number (5%, 1% or 0.1%) while the critical z-score is not.
Whereas a t-test is used for n30, where n=sample size. n < 30 or n > 30 is not entirely arbitrary; it is intended to indicate that n must be sufficiently large to use the normal distribution. In some cases, n must be greater than 50. Note, both the t-test and the z-test can only be used if the distribution from which the sample is being drawn is a normal distribution. A z-test can be used even if the distribution is not normal (but is not severely skewed) if n>30, in which case, we can safely assume that the distribution is normal.
z = 1.56 gives a 2-tailed interval for 88%.z = 1.56 gives a 2-tailed interval for 88%.z = 1.56 gives a 2-tailed interval for 88%.z = 1.56 gives a 2-tailed interval for 88%.
Z = ± 1.8119 gives a two-tailed interval of 93%
The answer will depend on whether the critical region is one-tailed or two-tailed.