Question

Find the P-value for the indicated hypothesis test with the given standardized test statistic, z. Decide whether to reject H0 for the given level of significance.

Two-tailed test with test statistic z= -1.94 and = 0.07.
P-value = ?

Answer 1

The p-value is the probability associated with a test statistic in hypothesis testing. To find the p-value for a two-tailed test, calculate the area to the left of the test statistic on a standard normal distribution and multiply it by two. Reject or fail to reject the null hypothesis based on whether the p-value is less than or greater than the level of significance.

Step-by-step explanation:

The p-value is the probability associated with a test statistic in hypothesis testing. In this case, we are given a two-tailed test with a test statistic of z = -1.94 and α = 0.07. To find the p-value, we calculate the area to the left of -1.94 on a standard normal distribution. We then multiply this probability by two to account for both tails. The p-value is calculated as 2 × P(Z < -1.94).

To decide whether to reject the null hypothesis (H0), we compare the p-value to the level of significance (α). If the p-value is less than α, we reject H0; otherwise, we fail to reject H0.

Answer 2

Reject H0 as the critical region for alpha = 0.07 is z ≤ -1.82 and z≥ 1.82

Step-by-step explanation:

For the significance level ∝ = 0.07

For a two tailed test we divide it with 2 and get 0.035

When we subtract 0.035 from 1 we get 0.965

And when we look at the z- table and corresponding to 0.965 we find the value of z to be 1.82

Now the calculated value of z= -1.94 which is less than ±1.82.

Hence reject H0 if z ≤ -1.82 and z≥ 1.82

Therefore reject H0.

While ∝ =0.07

p- value = 0.06 should be examined

the p- value is the smallest value of ∝ where we reject H0.

Hence at ∝= 0.06 critical region is z ≤ -1.88 and z≥ 1.88

At ∝= 0.05 critical region is z ≤ -1.96 and z≥ 1.96

So p- value is near 0.06