# Solution ho no significant difference in means

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Solution Ho: No significant difference in means between sample and population. We are given n = 16, (x- x ) 2 = 135, x = 41.5 and = 43.5 n 1 - n ) x - (x ( - x Z 2 16 1 - 16 135 43.5 - 41.5 3 4 20 = 2.67 Since t is more than the table value of 2.131 at t 0.05 for 15 d.f. Hence Ho is rejected. We conclude that the assumption of a mean of 43.5 inches for population is not reasonable.

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99 75 . 0 16 / 3 x SE 3 1) - (16 / 135 S 1 n ) x - (x S n S/ x SE 2 95 per cent fiducial limits for population mean x 0.05 at 15 d.f. (SE x ) is 41.5 2.131 0.75 41.5 1.598 39.902 and 43.098 Therefore, 39.90 and 43.098 Two Independent Samples Means Given two independent random samples of size n 1 and n 2 with x 1 and x 2 , and standard deviations S 1 and S 2 , we can calculate the statistic ‘t’ to test whether the samples have come from the normal populations. The Statistic t is defined. 2 1 2 1 2 1 n n n n s x - x t S= combined standard deviation 0 x - x when 2 n n n ) dx ( dx n ) dx ( dx 0 x - x when 2 n n ) x x ( ) x x ( S 2 1 2 2 2 2 1 2 1 2 2 1 2 2 2 2 1 1 Two Dependent Sample Means In the previous test, the two samples were independent. But there are many situations in which this condition does not hold true in the sense we have dependent samples. Two samples are said to be dependent in nature, if the elements in one sample are related to those in the other. The t-test for paired observations is defined as: 1 n n ) d ( d S or 1 n ) d d ( S S n d t 2 2
100 11.4. REVISION POINT 1 n n ) d ( d S or 1 n ) d d ( S S n d t 2 2 2 S n S n 2 1 2 2 2 2 1 1 n n 11.5. INTEXT QUESTION A group of 10 children were treated to find out how many digits they could repeat from memory after hearing them once. They were given practice for a week and were then tested. Is the difference between the performances of 10 children at the two tests significant. Child Test 1 Test 2 A B C D E F G H I J 6 5 4 7 8 6 7 5 8 8 7 7 6 8 9 6 9 7 8 10 11.6. SUMMARY By the end of this lesson, you should be able to understand t-test for single mean and two mean. The main aim of this Lesson is to study the Small sample test. 11.7. TERMINAL EXERCISES An IQ was administered to 5 persons before and after they were trained. The results are given below: Candidate IQ before training IQ after training 1 2 3 4 5 110 120 123 132 125 120 118 125 136 128 Test whether there is any change in IQ after the training programme. 11.8. SUPPLEMENTARY MATERIALS

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101 1) - levin-and-rubin-solution-manual 2) =MsQKG4Cu3xwC 11.9. ASSIGNMENTS 1) The average number of articles produced by two machines per day is 200 and 250 with standard deviation 20 and 25 respectively on the basis of records of 25 days production. Can you regard both the machines equally efficient at 0.01 level of significant?
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