What are the CRITICAL z-values that correspond to alphas of 1%, 5% and 10% for t

Question

What are the CRITICAL z-values that correspond to alphas of 1%, 5% and 10% for the LEFT TAIL and the RIGHT TAIL (6 numbers required)?

Now, split the alphas between both ends and give those pairs of values (right and left tails) for the these ? /2 (again, 6 numbers required).

What are the critical t-test values with 45 df at the 1%, %5 and 10% levels of significance?

Here are graphs showing the Normal (z-values) and the t-Distributions (t-with more than about 40 degrees of freedom looks like the Normal). The t or z-value separating the shaded and white sections can be either our calculated test statistic or the critical value that we compare the test statistic to (to see if we are in the “unusual” hence “reject” area).

For now let’s assume the indicated z and t values are the critical, decision making ones base on the level of significance (alpha) we have chosen. The values of ? are typically 1%, 5% or 10% . Graphs “a” and “b” represent ONE-TAILED tests, hence the area in the shaded region of graph “b” represents the 1%, 5% or 10% probabilities. We would use this critical t or z value for RIGHT TAILED tests, where the NULL hypothesis would be something like the mean is less than or equal to 3.5 (m < 3.5) and the ALTERNATE hypothesis would be that the mean is greater than 3.5 (m > 3.5). The NULL MUST have an equality in it.

To find the critical value of z, we go to the Table and look for the z-value that corresponds to 99% (0.9900), 95% (0.9500) or 90% (0.9000) depending on which alpha we chose. Then, if our calculated test statistic is a larger number than the critical value, we would REJECT Ho and accept the alternate hypothesis. To find the critical t-value, we first need to calculate the DEGREES OF FREEDOM (but if greater than about 40 we can use the z-table). This all is for a one-tailed test to the right

If your NULL were that the mean were greater than or equal to 3.5 (ALTERNATE is that the mean is less than 3.5) our critical value would be in the LEFT TAIL and we would want to determine if our test statistic is LESS than the critical value (a test statistic of -0.62 is less than a critical value of -0.61, hence we would REJECT Ho).

Graphs “c” and “d” are for TWO-TAILED tests in which the NULL hypothesis is simply that the mean equals 3.5 ( no < or >) and the ALTERNATE is that the mean is simply NOT EQUAL to 3.5. In this case we must split the alpha between the two tails. So an alpha of 5% becomes 2.5% at each tail. So for the right shorter tail we need an area of 97.5% (0.9750) to the left and for the left shorter tail we need an area of simply 2.5% (0.2500). For and alpha of 1% this would be 0.5% (0.0500) at the left tail and 99.5% (0.9950) to the left to determine the right tail. You can figure this for an alpha of 10% split between both tails.

Explanation / Answer

What are the CRITICAL z-values that correspond to alphas of 1%, 5% and 10% for the LEFT TAIL and the RIGHT TAIL (6 numbers required)?

Using tables, for left tail:

1% : zcrit = -2.33
5% : zcrit = -1.64
10% : zcrit = -1.28

Using tables, for right tail:

1% : zcrit = 2.33
5% : zcrit = 1.64
10% : zcrit = 1.28

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What are the critical t-test values with 45 df at the 1%, %5 and 10% levels of significance?

As df = 45, using tables, ads this is two tailed,

1%: tcrit = -2.690, 2.690
5%: tcrit = -2.014, 2.014
10%: tcrit = -1.679, 1.679 [ANSWER]

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