Question

If a directional, .05 level of significance (predicted ‘lower than’) had been chosen, what z-score would be needed for the difference between X and µ to be significant?

A. -1.65

B. -1.96

C. -2.33

D. +/- 1.65

If the probability of finding a difference that really does exist is .65 (correctly rejecting the null hypothesis when the null hypothesis really is false), what is the probability of the Type II error?

A. .05 B. .95 C. .35 D. .65 also

Answer #1

From standard normal tables, we get:

P( -1.96 < Z < 1.96 ) = 0.95

Therefore -1.96, 1.96 are the critical values here.

As the value -2.33 < -1.96, therefore **-2.33 lies
outside the given interval and therefore is a significant
value.**

The probability of type II error is the probability of retaining the null hypothesis when it is false. We are given the probability of rejecting a false null hypothesis as 0.65, therefore probability of retaining would be 1 - 0.65 = 0.35

**Therefore 0.35 is the required probability
here.**

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