STAT - Comparing two populations These notes relate with...

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Comparing two populations These notes relate with the chapter 9 of your text book. AUTHOR: ATUL ROY We are going to look at comparison of two population means. We shall do very basic level calculations, to understand the idea because in practice mostly such work is done by using computational packages. Example 1: A big apartment rental company with many buildings uses a battery of type ”A” for their fire alarm. Another brand ”B” claims that their batteries will last longer than ”A.” To test this claim at 1% level of significance, 40 batteries of brand ”A” and 42 batteries with brand ”B” are tested in similar environment and the results are (time in hours) mean standard deviation sample size A 1015 89 40 B 1032 91 42 If A is the overall mean for the life of the brand ”A” and If B is the overall mean for the life of the brand ”B” H o : A B A B 0 H A : A B A B 0 Test statistic: z x A x B A B A 2 n A B 2 n B 1
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sample sizes are larger than 30 We may use the sample standard deviation for the population standard deviation z 1015 1032 0 89 2 40 91 2 42 0 . 8551553802 P_value is the area under the z-curve to the left of z 0.86 FRom the z-table, this area is 0 . 1949 P_value is not less than 0.01 Do not reject the null The results are not significant at 1% level The above is an Example of a Two sample test for two population means, when the samples are independent. Using a TI-83plus Use STAT and select TESTS 2
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Select 3
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Ask it to calculate 4
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...................... What if one (or both) of the sample sizes is smaller than 30 May use t-test under the assumption that both the populations are normal and that the samples are independent. Example 2: (This is a corrected version) A fruit juice bar uses mangoes of brand ”A” to make its Mango Juices. Another brand ”B” claims that their mangoes will give more pulp. To test this at 5% level of significance, the pulps from 16 randomly selected magoes of the brand ”A” are weighed and also the pulps from 18 randomly selected mangoes of brand ”B” are weighed. Here are the results (weights in grams) 5
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mean standard deviation sample size A 89.7 7.6 16 B 97.8 6.9 18 Assuming a normal distribution for the weights of the mangoes and independent selection of samples H o : A B A B 0 H A : A B A B 0 t x A x B A B n A 1 s A 2 n B 1 s B 2 n A n B 2 1 n A 1 n B the degrees of freedom here is n A n B 2 (using the methods on the page 377 in the text) t 89.7 97.8 0 16 1 7.6 2 18 1 6.9 2 16 18 2 1 16 1 18 3. 257688747495732303 df is 16 18 2 32 Go to the t-table and note that .05 32 1.694 This means that the area under the t-curve to the left of at 32 degrees of freedom is 0.05 s t
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This note was uploaded on 09/22/2011 for the course STAT 101 taught by Professor Unknown during the Fall '08 term at Alabama State University.

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STAT - Comparing two populations These notes relate with...

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