Finding P-Values
In Exercises 13–16, do the following:

Question

Finding P-Values

In Exercises 13–16, do the following:

i. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

ii. Find the P-value. (See Figure 8-3.)

iii. Using a significance level of α = 0.05 should we reject H0 or should we fail to reject H0?

The test statistic of z = -0.75 is obtained when testing the claim that p<1/3.

Accepted Answer

Hi everyone, let's take a look at this practice problem. This problem says, consider a hypothesis test for the proportion of a population where the test statistic obtained is Z is equal to -1.45. The claim being tested is that the population proportion is greater than 0.4. There are three parts to this problem. For part one, determine whether the test is two-tailed, right-tailed, or left tailed. For part two, calculate the P value for this test, and for part 3, at a significant level of alpha equal to 0.05, should we reject the null hypothesis or fail to reject it. So the first thing we need to do is write down our hypothesis. So for a null hypothesis, H not. We're going to have that E is less than or equal to 0.4, and for our alternative hypothesis, H1, we're going to have that P is greater than 0.4, where P here is our population proportion. So, for part one, we need to determine whether the test is two-tailed, right-tailed, or left-tailed. And so here the hypothesis test is focused on whether the population proportion is greater than 0.4. And so since the alternative hypothesis test for a value that's greater than 0.4, that means that this is a right-tailed test. So the answer for part one is going to be right tailed. And so now we can move on to part 2. Now for part 2, we need to calculate. The P value for this test. And we're given a Z value that is equal to -1.45. So, if we look in our standard normal distribution table, we see that the area to the left of the D score is approximately 0.0735. So, for a right tail test, or P value, is going to be equal to 1 minus the value that we had in the table of 0.0. 735. And so, evaluating this expression, this is going to be equal to. 0.9265. So that is going to be our answer for part 2. And finally, for part 3. At a significant level of alpha equal to 0.05, should we reject the hypothesis or fail to reject it. So recall that if the P-value is less than or equal to alpha, then we reject the null hypothesis. Or, or if the P value is greater than alpha, then we fail to reject the null hypothesis. So, in our case here, our P value of 0.9265 is greater than alpha, which is 0.05. So that means that we fail. To reject our null hypothesis. So we fail to reject each knot. So that is going to be the answer for part 3. So I hope that this explanation has been useful, and I'll see you in the next video.

Key Concepts

Hypothesis Testing

P-Value

One-Tailed vs. Two-Tailed Tests

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