Question

If you use a 0.10 level of significance in a two-tail hypothesis test, what is your decision rule for rejecting a null hypothesis that the population mean equals 500 if you use the Z test

Answer 1

Answer:

If the value of our test statistics is less than the critical values of z at a 5% level of significance (where critical values are -1.645 and 1.645), then we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

If the value of our test statistics is more than the critical values of z at a 5% level of significance (where critical values are -1.645 and 1.645), then we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

Step-by-step explanation:

We are given that the population mean equals 500 and we use a 0.10 level of significance in a two-tail hypothesis test.

Let $\mu$ = population mean.

So, Null Hypothesis, $H_0$ : $\mu$ = 500

Alternate Hypothesis, $H_A$ : $\mu$ $\neq$ 500

Here, the null hypothesis states that the population mean is equal to 500.

On the other hand, the alternate hypothesis states the population mean is different from 500.

Now, firstly we should note that for the two-tailed test, the level of significance to be taken is ($\frac{\alpha}{2}=\frac{0.10}{2}$) = 0.05 or 5%.

So, the decision rule for rejecting a null hypothesis is given by;

• If the value of our test statistics is less than the critical values of z at a 5% level of significance (where critical values are -1.645 and 1.645), then we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

• If the value of our test statistics is more than the critical values of z at a 5% level of significance (where critical values are -1.645 and 1.645), then we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.