1. A study of 98 investment advisors asked them to predict the value of a "penny" stock a week ahead. The correlation between the values predicted and the actual value was 0.20. Was this evidence that they could predict penny stock performance?
a) State the null and alternative hypotheses about the cor- relation.
b) Calculate the test statistic.
c) Perform the test at a = 0.05.
2. For a physical exam to qualify for company-provided insurance, 14 employees had their blood pressure mea- sured. Their Systolic and Diastolic BP are given here;
|
SBP
|
DBP
|
|
140
|
90
|
|
208
|
114
|
|
140
|
90
|
|
164
|
104
|
|
142
|
88
|
|
124
|
82
|
|
120
|
80
|
|
142
|
72
|
|
160
|
90
|
|
142
|
98
|
|
225
|
125
|
|
140
|
90
|
|
220
|
114
|
|
150
|
85
|
A regression, found with technology, reports an R2 of 81.3%.
a) Make a scatterplot of the data. Is it appropriate to inter- pret correlation?
b) State the null and alternative hypotheses about the correlation.
c) Calculate the test statistic. (Hint: Remember the relationship between correlation and R2.)
d) Perform the test at a = 0.01 and state your conclusion.