Question: The problem I struggled with this week is 8.1.27. It seemed like all the rest of the problems in the first chapter, but I got it wrong because I used “0” instead of the µ1-µ2 value. Not sure when I am supposed to use that value or how it is determined. I used the “view an example” feature to figure out I was supposed to put it in there for the homework, but I am worried about the quiz and not being able to recognize the situation it is needed.
Answer: When we are comparing two samples, whether means or proportions pay close attention to the claim. Here, the claim is that the difference in the two mean salaries is more than $5000. That requires the claim to be the alternative hypothesis since “more than” is a > operator, which is an inequality. So, Ha: μ1 – μ2 > $5000.
I know. You are saying that you don’t see a claim. But when a problem asks a question as this one does, that is the claim to be tested unless you find a more definitive claim later in the problem.
Note that you need to follow the “standard” format which is that we consider μ1– μ2 and not the reverse because that is the way the claim is stated in the problem: Region 1 is mentioned before Region 2. I think it might be less confusing if the problem had compared Alabama and Florida salaries, but the first entity (population) mentioned is logically μ1.
Here is the StatCrunch solution: [Read more…] about Pick-a-Problem: What difference does it make? 8.1.27
Question: I have hit the wall on a simple problem. I seem to be hitting these more often now.
At any rate. 8.1.11, the difference between two means hypothesis test standardized test statistic requires µ1 – µ2. So, how does one calculate this when we are never given a value for μ? I used 0 for the values, and came out with the WRONG answer. Request a nudge in the right direction.
Answer: James, for most of our mean difference problems, we will not be given the assumed population means or the mean difference. If not, you use 0 for the mean difference. In your problem, you are told that μ1 = μ2, so the mean difference μ1 – μ2, is 0.
Here is the StatCrunch solution with slightly different summary data:
If you are given summary data and asked to find a confidence interval, it is relatively easy using StatCrunch. Here is a typical problem:
In this problem, you are told to use the t-distribution, but that may not always be the case. If you are given the sample standard deviation, s, instead of the population standard deviation, σ , use the t-distribution to find the confidence interval. In StatCrunch, this is in the T Stats menu. If you are given σ or are told to use the z-distribution, it is essentially the same steps except you select Z Stats in step 2.
Download a PDF for your notes: Confidence Interval for a Mean using StatCrunch
Here is the screenshot of the basic StatCrunch solution.
[My Excel calculator for running this test is found here.]
As always for proportion problems, we have to check first to be sure np and nq or n*(1-p) are both > 5.
If they are, we can use the normal approximation to the binomial (a proportion is essentially a binomial test). That is why for all the proportion problems we do in this course we use the z-test. If either np or nq is not > 5, we have to use a test that is beyond the scope of this course.
Step 1 as almost always is true for us, is to click on Stat once StatCrunch is open. The sequence is Stat>Proportion Stats>One Sample>With Summary. Then enter the number of success, which is just n*p, the sample size, select the Hypothesis test for p, and enter the null hypothesis and select the math operator for Ha. Click Compute! The answer window opens and you can see the test statistic of z= -1.042 and the p-value of 0.29. Although this problem asks us to find the critical value and make our decision based on that, the p-value always agrees and tells us we Fail to Reject the null since p>α.
I used the Stat>Calculators>Normal path to bring up the normal calculator. Because this is a two-tailed test (recall Ha has the ≠ math operator), I like to use the Between button and enter the confidence level c, which is 1-α or 0.9. The calculator shows the two critical values and rejection areas. Because the test statistic of -1.042 does not fall in either rejection area, we get the same decision of Fail to Reject the null.
I have a video here on solving combination and permutations problems using StatCrunch, but here is the basic Excel solution for problem 3.4.51 in MyStatLab homework which just requires the use of combinations since order does not matter.
Remember the fundamental counting principle says that if Event A can occur in m ways and Event B can occur in n ways, the number of ways Event A and Event B can occur is m*n.
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