Question

Hydrogen content is conjectured to be an important factor in porosity of aluminum alloy castings Antidelves the accompanying data on content andy a porosity for one particular measurem x y 0.18 0.46 0.20 0.71 0.21 0.40 0.21 0.21 0.22 0.43 0.53 0.4 0.23 0.24 0.23 0.40 0.24 0.20 0.24 0.2 0.25 0.28 0.18 0.68 0.30 0.71 0.37 0.77 Minitab gives the following output in a response to a Correlation command: Correlation of Hydecon and Porosity = 0.451 (a) Test at level 0.05 to see whether the population correlation coefficient differs from State the appropriate and alternative hypotheses HIPO HIPO Hoi po Hipo Hy P=0 HO Calculate the test statistic and determine the value Round your best statistic to two decimal places and you State the conclusion in the problem context Fall to reject The data does not suggest that the population correlation coefficient differs cantly from 0. Reject The data does not s et that the population correlation co n t differs significantly from a Fall to reject the data suggests that the population correlation co n t different cantly from o Reject The data w a s that the population correlation coefficient de signalcantly from and your answer to de (6) regreson analysis had been carried out what percentage of observed variation in prsty could be attributed to the model relation

Answer 1

a)

correlation hypothesis test  
Ho:   ρ = 0
Ha:   ρ ╪ 0

n=   14                          
alpha,α =    0.05                          
correlation , r =   0.4510                          
                              
Df =    n-2 =   12                      
t-test statistic = r*√(n-2)/√(1-r²) =        0.4510   * √    12   / √ ( 1 -    0.4510   ² ) =   1.75

t=1.75

p-value =    0.106   [excel function: =t.dist.2t(t-stat,df) ]   

decision:   p value > α , so, do not reject the null hypothesis  

fail to reject Ho. the data does not suggest that population correlation coefficient differs significantly from 0

b)

R²=0.4510² = 0.2034

answer: 20.34%