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Question: A teacher wishes to know whether there is any relationship between the hours of study and the test scores of the students. Ten students were selected randomly and were given a test. Test the hypothesis that there is a significant relationship between hours of study and test scores at α = 0.01 using the P-value method and determine the equation of the regression line and predict the value for y x Hours of study (x 6 11 8 11 12 14 15 7 12 6 Test scores (y 50 75 65 70 78 85 90 65 80 55
y x y x y x y x Steps to derive 1 Make a table with values for x y x 2 , y 2 , xy 2 r n ( Σ x y ) - ( Σ x ) ( Σ y ) [ n ( Σ x 2 ) - ( Σ x ) 2 ] [ n ( Σ y 2 ) - ( Σ y ) 2 ] 3 r 4 Therefore, r 5 State the hypothesis: H0 : ρ = 0 and H1 : ρ ≠ 06 Compute the test value, t r n - 2 1 - r 2 7 We can see that the t 8 Hence, P - value falls beyond 0.01, i.e., P - value < 0.01, reject the null hypothesis, since P - value < 0.019 Therefore, there is a significant relationship between the hours of study and the test scores.10 Regression line equation is y a + bx a ( Σ y ) ( Σ x 2 ) - ( Σ x ) ( Σ x y ) n ( Σ x 2 ) - ( Σ x ) 2 b n ( Σ x y ) - ( Σ x ) ( Σ y ) n ( Σ x 2 ) - ( Σ x ) 2 11 a b 12 Therefore, the equation of the regression line y a + bx y x 13 When x y Hence the right answer is Option C Click Here To Go Back In which year is the population of Mid west and North west the same?.. The population of New York is _______ the population of Los Angeles in the year 1980... 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