SOLUTION: A psychologist is studying the self image of smokers, as measured by the self-image (SI) score from a personality inventory. She would like to examine the mean SI score,μ,for the

Question 1181648: A psychologist is studying the self image of smokers, as measured by the self-image (SI) score from a personality inventory. She would like to examine the mean SI score,μ,for the population of all smokers. Previously published studies have indicated that the mean SI score for the population of all smokers is 85 and that the standard deviation is 10, but the psychologist believes that the value for the mean has decreased. She plans to perform a statistical test. She takes a random sample of SI scores for smokers and computes the sample mean to be 79.
Based on this information, answer the questions below.
1. What are the null hypothesis (H0) and the alternative hypothesis (H1) that should be used for the test?
2. In the context of this test, what is a Type II error?
A Type II error is ____ ____ the hypothesis that μ is ____ ____ when, in fact, μ is ____ _____.

3. Suppose that the psychologist decides to reject the null hypothesis. What sort of error might she be making?

I don't really understand where to start with these kind of problems or I would show some sort of work. I would actually like to know if this could be done in excel? Thats how I do most of my statistics. Thank you
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
Type II errors are errors of omission where one accepts a false null hypothesis.
Here, Ho is mean SI score is 85 or higher
Ha is the mean SI score is lower.
If one rejects Ho, a type I error is saying the the score is lower when it really is the same or even higher. One is overcalling an error.
If one accepts a false Ho, the conclusion is the score is higher when it isn't. One is missing the error.
So the error is accepting the null hypothesis that the mean is the same (or higher) when the mean is lower.
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Rejecting Ho will either be correct or lead to a Type I error.
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Yes, you can do this in Excel. I like the TI-83 a lot better at least for checking the calculations if not for outright doing them.
Here, the calculation will be z=(79-85)/(10/sqrt(n), and compare that to the critical value z that is chosen.
This doesn't need to be done in Excel, unlike tables (Chi-Square), large data sets for mean and sd, analysis of variance.
Most of what you will be doing is dealing with Type I error. Power to show a difference when it really exists has to do with Type II error, which often occurs when the sample size is too small to show a true difference, and one fails to reject when one should.
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