9.8 THE VIDEO GAME SATISFACTION RATING CASE Recall that “very satisfied” custome
ID: 2960227 • Letter: 9
Question
9.8 THE VIDEO GAME SATISFACTION RATING CASERecall that “very satisfied” customers give the XYZ-Box video game system a rating that is at least 42. Suppose that the manufacturer of the XYZ-Box wishes to use the random sample of 65 satisfaction ratings to provide evidence supporting the claim that the mean composite satisfaction rating for the XYZ-Box exceeds 42.
a Letting m represent the mean composite satisfaction rating for the XYZ-Box, set up the null and alternative hypotheses needed if we wish to attempt to provide evidence supporting the claim that µ exceeds 42.
b In the context of this situation, interpret making a Type I error; interpret making a Type II error.
(Bowerman. Custom book for Ashford: Essentials of Business Statistics. McGraw-Hill Primis Custom Publishing, 38503. p. 377).
<vbk:0390107115#page(377)>
Explanation / Answer
(a) The test hypothesis is
Ho:<=42
Ha:>42
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(b)
A Type 1 error would mean accepting the claim that the mean is greater than 42 or 42.5 when that is not true. We affirm that the average rating is very satisfied when that is not the case.
A Type 2 error would mean that the average rating is very satisified but we did not draw that conclusion. Thus an average rating in our sample of 45 might not be enough for us to conclude the true average is more then 42 at say a 0.01 certainty level. We would not reject the null hypothesis with confidence--but we would certainly not conclude that the null hypothesis is true, A type 2 error involves a failure to draw a correct conclusion lacking strong enough evidence. It is not entirely clear that this should even be called an error.
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