Testing for correlation Problem set A Answers

1. (a) H0: ρ = 0, H1: ρ > 0. ρ is the population correlation coefficient between pages read per week and vocabulary mark.
2. (b) H0: ρ = 0, H1: ρ < 0. ρ is the population correlation coefficient between steepness of a hill and average cycling speed.
3. (c) H0: ρ = 0, H1: ρ ≠ 0. ρ is the population correlation coefficient between monthly rainfall and milk yield per cow.

r = 0.615, p = 0.0524

p = 0.0417, reject H0: sufficient evidence of negative correlation

p = 0.472, do not reject H0: insufficient evidence of correlation

1. (a) Both variables are normally distributed.
2. (b) An elliptical cloud suggests two variables that are both roughly normal, so the assumption is reasonable.

p = 0.0133, reject H0: sufficient evidence of positive correlation

1. (a) H0: ρ = 0, H1: ρ < 0. ρ is the population correlation coefficient between sessions per week and resting heart rate.
2. (b) r = −0.802, p = 0.00832
3. (c) p = 0.00832 < 0.05, so reject H0. There is sufficient evidence at the 5% level of negative correlation between sessions per week and resting heart rate.

1. (a) r = 0.407
2. (b) p = 0.277, so do not reject H0. There is insufficient evidence at the 1% level of correlation between ticket price and audience size.

p = 0.790, do not reject H0; r = 0.334 is positive, so the data go against the belief

1. (a) p = 0.0265, reject H0: positive correlation
2. (b) p = 0.0530, do not reject H0
3. (c) The two-tailed test splits the 5% between two tails, so a result in one tail needs to be more extreme to be significant.