Testing for correlation Problem set B Answers

1. (a) H0: ρ = 0, H1: ρ > 0. ρ is the population correlation coefficient between weekly hours of sunshine and number of tomatoes harvested.
2. (b) H0: ρ = 0, H1: ρ < 0. ρ is the population correlation coefficient between the temperature and cups of hot chocolate sold.
3. (c) H0: ρ = 0, H1: ρ ≠ 0. ρ is the population correlation coefficient between a town's population and number of libraries.

r = 0.689, p = 0.0294

p = 0.0498, reject H0: sufficient evidence of negative correlation

p = 0.467, do not reject H0: insufficient evidence of correlation

1. (a) Both variables are normally distributed.
2. (b) A strongly skewed variable is not normal, so the p-value may not be reliable.

p = 0.00224, reject H0: sufficient evidence of positive correlation

1. (a) H0: ρ = 0, H1: ρ < 0. ρ is the population correlation coefficient between distance from the city centre and monthly rent.
2. (b) r = −0.780, p = 0.0113
3. (c) p = 0.0113 < 0.05, so reject H0. There is sufficient evidence at the 5% level of negative correlation between distance from the city centre and monthly rent.

1. (a) r = 0.510
2. (b) p = 0.161, so do not reject H0. There is insufficient evidence at the 1% level of correlation between price of a cycle helmet and customer rating.

p = 0.771, do not reject H0; r = 0.308 is positive, so the data go against the belief

1. (a) p = 0.0431, reject H0: positive correlation
2. (b) p = 0.0862, do not reject H0
3. (c) A two-tailed test needs stronger evidence, because the 5% is shared between two tails.