Dawn Wright, Ph.D.

Learning, Statistics, and me

hypothesis test

Pick-a-Problem: Not given values for µ in 8.1.11

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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:

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Finding Critcal Values and Degrees of Freedom

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Many students struggle to find critical values of z, t, and Chi-square for hypothesis tests. No matter how often I show them how to use the StatCrunch calculators to do this, they gravitate back to the tables. And make a lot of mistakes. To help a bit, I have created some Excel calculators that should make it a bit easier. A minimum of data/info is needed to use the calculators. First, you need to know which distribution you need and I have covered this in other posts. For the z, you just need to know alpha and the tail of the test which is always indicated by the math operator in the alternative hypothesis. For the t, things get a bit more complicated as you also need to know the sample size(s) and whether or not the variances are assumed to be equal if you are dealing with a two-sample test. Note you can use these calculators to find the degrees of freedom for the different tests too.

I have embedded the Critical Values workbook below. In each, you enter your data in the blue cells and all answers show up in yellow cells. In some, you will need to select options in an orange cell.  As an example of how they work, here is how to use the Two Independent Samples Critical Values calculator:

This is the index of calculators.

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Single-sample Hypothesis Test for a Proportion

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Consider the following problem statement:

An article in an online magazine states that 40% of home buyers found their real estate agent through referrals by a friend. However, a professor in a local college sampled 1000 home buyers and found that 426 chose an agent recommended by a friend.

Does the data refute the claim made by the magazine? Use a significance level of 0.02.

Solution:

  • First, you should recognize that this is a test about a single proportion, not a mean or other statistic.
  • The claim is that the proportion of home buyers who select their real estate agent based on the recommendation of a friend is 0.40. Therefore, the claim is p = 0.40.
  • Since the claim contains an equality, =, it must be the null. Ho: p = 0.40.
  • The alternative must be the complement, Ha: p ≠ 40.
  • Remember the rule of thumb is that all hypothesis tests for proportions are z-tests. But you should confirm that you can use the normal distribution by checking that both n*p and n*q are greater than 5. Here n*p = 2000*0.40 = 800 and n*q = 2000*(1-0.40) = 1200. Both are > 5, there we can use the normal distribution.
  • I recommend always sketching the situation described in the problem. Here we see that the sample count of 426 falls on the right side of the hypothesized mean of 400 for the population. Recall, the mean for a proportion is just the n*p or 0.4 * 1000. The standard deviation for a proportion is

[Read more…] about Single-sample Hypothesis Test for a Proportion

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How to determine the tail of a hypothesis test

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[embedyt] http://www.youtube.com/watch?v=fgbChDkU4sQ[/embedyt]
A quick and easy way to know whether you have a right-tailed, left-tailed, or two-tailed hypothesis test.

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