Question

5 7 8 10 11 12 Suppose a teacher recorded the attendance of her students in a recent statistics class because she wanted to investigate the linear relationship between the number of classes they missed and their final grades. The accompanying table shows these data for a random sample of nine students. Complete parts a through c. Click the icon to view the table showing missed classes and final grade. a. Calculate the correlation coefficient for this sample. The correlation coefficient is (Type an integer or decimal rounded to three decimal places as needed.) b. Using a = 0.01, test to determine if the population correlation coefficient is less than zero. The hypotheses for this test are The test statistic is (Type an integer or decimal rounded to two decimal places as needed.) The p-value is (Type an integer or decimal rounded to three decimal places as needed.) Therefore, at the 0.01 level of significance, the null hypothesis. There sufficient evidence to conclude that the population correlation coefficient is c. What conclusions can be made based on these results? 19 20 21 22 23 24 25 26 27 zero. 28 The conclusion is that there linear relationship between missed classes and final grade. Enter your answer in each of the answer boxes. 2 35

Answer 1

(Note to student : Since you have not provided options to the blanks, I am completing the statement with logical answers. Use the options closest to the answers.)

a)   Correlation coefficient is calculated using Excel tool Data -> Data Analysis -> Correlation                          
   We get                           
   r = -0.660                          
   The correlation coefficient is -0.660                          
                              
b)   The hypotheses for this test are                          
   Ho : r = 0   or   Ho : r ≥ 0   (…Choose as per given options)              
   H1 : r < 0                        
                              
   Test Statistic                          
   Degrees of freedom = df = n - 2 = 9 - 2 = 7                          
   Test statistic t is given by                          
      
   t = -2.32                          
   The test statistic is -2.32                          
                              
   p-value                          
   This is a left tailed test since the alternative hypothesis contains the less than sign                          
   p-value is found using Excel function t.dist                          
   p-value = t.dist(t, df, TRUE)                          
                   = t.dist(-2.32, 7, TRUE)                          
   p-value = 0.027                          
   The p-value is 0.027                          

t=r n-2 1-p2 t= (-0.660) 9- 2 1-(-0.660)2

    α = 0.01
   0.027 > 0.01,   that is, p-value is greater than α                          
                              
   Therefore at the 0.01 level of significance, Do Not Reject the null hypothesis.                          
   There does not exist sufficient evidence to conclude that the population                           
   correlation coefficient is less than zero                          
                              
                              
c)   The conclusion is that there is no linear relationship between missed classes and final grades                                            (…Choose as per options given)              

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