ST_203_tute_7 - DEPARTMENT OF STATISTICS AND COMPUTER...

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DEPARTMENT OF STATISTICS AND COMPUTER SCIENCE THEORY OF STATISTICS- ST 203 ACADAMEIC YEAR 2012/2013, SEMESTER II TUTORIAL NO: 7 -(Date of submission: November 27, 2013) 1. (a) Define the significance level α and power of the test 1- β in statistical test of hypotheses. (b) A random sample of 20 observations is selected from a binomial population with unknown proportion of success. Suppose we wish to test the hypothesis H 0 : p=0.8 vs. H 1 : p<0.8. , and assume that the rejection region y<12 is used. (i) Find α. (ii) Find β when p=0.6. (iii) Find the rejection region of the form y c so that 0.01. (iv) For the rejection region in (iii) find , when p = 0.6. 2. Oak trees of a certain type have an average growth of 11.3 inches in 3 years under a specific environment. A botanist claims that a new type will have greater average growth in the same time period under the same condition. A sample of 15 trees of the new type was observed and the following measurements were taken. 12.7, 14.8, 9.0, 13.3, 12.3, 13.5, 13.5, 12.3, 10.0, 11.3, 9.9, 9.2, 9.4, 13.0, 9.6 (i) Using MINITAB draw a normal probability plot, and use Anderson-Darlings test to check the normality of the data. Interpret the results.
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