A financial analyst asked the following question: 'Is the average earnings yield of manufacturing companies the same as the average earnings yield of retailing companies?' To examine this question, the analyst randomly sampled 19 manufacturing companies and 24 retailing companies. The descriptive statistics from each sample of companies are as follows:
|
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Manufacturers
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Retailers
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|
Sample mean (%)
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8.45
|
10.22
|
|
Sample standard deviation
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3.32
|
4.14
|
|
Sample size
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19
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24
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(a) Formulate the null and alternative hypothesis for this management question (i.e. can the financial analyst conclude that there is no difference in the average earnings yield between companies in the manufacturing and retailing sectors?)
(b) Conduct a hypothesis test for the difference between two means to test the null hypothesis at the 5% level of significance. What conclusion can be drawn?