In Exercises 11 and 12, find the P-value for the hypothesis te...

Question

In Exercises 11 and 12, find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance α.

Two-tailed test, z = 2.57, α = 0.10

Accepted Answer

Hello everybody. Let's take a look at this next problem. For a two-tailed hypothesis test, the standardized test statistic is Z equals 1.96, and the significance level is alpha equals 0.01. What is the P value, and do you reject the null hypothesis? And our answer choices are A 0.0250, yes, B 0.0500, yes, C 0.0500 no, and D 0.0250, no. So, let's recall what our graph looks like for a two-tailed hypothesis test. So draw a little Distribution there So I just wanted to make my central line and dash line there. And we have that Z equals 1.96. So, we'll draw a line. Somewhere, again, doesn't have to be, we're just gonna estimate, we'll say at this point Z equals 1.96. And we have that significance level alpha equals 0.01. So, what do we mean by the P value when we have a two-tailed test? Well, I'll highlight in blue, we're going to refer to this area to the right of our positive Z, but then we know that we have another corresponding value on The other side of that distribution curve, so there will be another z line. Corresponding to -1.96. And for PI, we're gonna need to add in the area to the left of that Z line. So both of these outlying areas. So, first, we calculate the P value for one of these Z values, and then we multiply by 2. Now, it's a little easier to get a P value from a Z table. We'll say we're going to calculate that P value from a Z table. If we use that negative Z value, because recall that those tables always give us the area to the left of our line there. So, a little bit easier to work with a negative Z value. And we can do that because, again, we have this two-tailed hypothesis test. So, we'll look at the Z value for the negative 1.96. So, take a, you can look that up, or wait for me to put it here. So, pause if you want to look it up on your own. But we will get a P value here equivalent to 0.0250. However, we know that to calculate. The value for a two-tailed test. Because this P value I looked up from my table would only be a left tailed test. I need to multiply 2. And multiply that by 0.250, since we have the area on the outside of the curve on both sides. So in that case, our P value will equal. 0 point. 0500. So you see that in terms of our answer choices, we can rule out choice C, or excuse me, choice A, since that has 0.0250, and choice D for the same reason. So we go between B or C. So, we have our P-value for this two-tailed test. And we need to say, do we reject I don't know hypothesis. So recall that, that means. We need to compare this p-value to our alpha that we're given. So, our P value of 0.0500. is greater than our alpha value of 0.01. And that means that we do not have sufficient evidence to reject our hypothesis. We essentially don't have an unusual enough sample to allow us to do that. So our answer is going to be choice C 0.5. Excuse me, 0.0500 is our calculated P value for a two-tailed hypothesis test. And then with a significant level of 0.01, we do not reject the null hypothesis, our answer is no. So, choice C is the answer to this question, where we have a two-tailed hypothesis with Z equals 1.96. See you in the next video.

In Exercises 11 and 12, find the P-value for the hypothesis test with the standardized test statistic z. Decide whether to reject H0 for the level of significance α.

Two-tailed test, z = 2.57, α = 0.10

Key Concepts

P-value

Hypothesis Testing

Significance Level (α)

Watch next