ECN 206E PS#9.pdf

# ECN 206E PS#9.pdf - ECN 206E Statistics II Problem Set 9...

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ECN 206E — Statistics II Problem Set 9 Spring ’18 Exercise 14.1 A random sample of 150 residents in one community was asked to indicate their first preference for one of three television stations that air the 5 p.m. news. The results obtained are shown in the following table. Test the null hypothesis that for this population their first preferences are evenly distributed over the three stations. Station A B C Number of first preferences 47 42 61 Answer: H 0 : First preferences are evenly distributed over the three stations. H 1 : Otherwise Station A B C Total Observed Number of first preferences 47 42 61 150 Probability ( H 0 ) 0.3333 0.3333 0.3333 1.000 Expected Number 50 50 50 150 Chi-Square calculation 0.18 1.28 2.42 3.88 Chi-square calculation: χ 2 = ( O i - E i ) 2 E i = 3 . 88 χ 2 2 , 0 . 10 = 4 . 61; Therefore, fail to reject H 0 at the 10% level. Exercise 14.6 A campus administrator has found that 60% of all students view courses as very useful, 20%, as somewhat useful, and 20%, as worthless. Of a random sample of 100 students taking business courses, 68 found the course in question very useful, 18, somewhat useful, and 14, worthless. Test the null hypothesis that the population distribution for business courses is the same as that for all courses. Answer: H 0 : Student opinion of business courses is the same as that for all courses. H 1 : otherwise Opinion Very Useful Somewhat Worthless Total Observed Number 68 18 14 100 Probability ( H 0 ) 0.6 0.2 0.2 1 Expected Number 60 20 20 100 Chi-Square calculation 1.066666667 0.2 1.8 3.066667 Chi-square calculation: χ 2 = ( O i - E i ) 2 E i = 3 . 067 χ 2 2 , 0 . 10 = 4 . 61; Therefore, do not reject H 0 at the 10% level. 1/6 T.A. Bu˘ gra Aky¨uz

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ECN 206E — Statistics II Problem Set 9 Spring ’18 Exercise 14.18 University administrators have collected the following information concerning student grade point average and the school of the student’s major.
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• Fall '17
• Null hypothesis, Non-parametric statistics, T.A. Bu˘gra Aky¨, ECN 206E

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