Samples of four rainbow trout and four largescale suckers taken from the Spokane River were tested for lead and zinc content in milligrams per kilogram.
a. Use software to regress zinc on lead content for rainbow trout; first report the P-value.
b. State whether or not there is statistical evidence of a relationship for trout. If there is evidence of a relationship, state whether it appears to be positive or negative; strong, moderate, or weak.
c. Use software to regress zinc on lead content for largescale suckers; first report the P-value.
d. State whether or not there is statistical evidence of a relationship for suckers. If there is evidence of a relationship, state whether it appears to be positive or negative; strong, moderate, or weak.
e. Is it better to regress lead on zinc, or zinc on lead, or are they equally good?
f. If we did regress lead on zinc, instead of zinc on lead, would this affect the equation of the regression line, or the value of r, or both of these, or neither of these?
g. For rainbow trout, use the sample slope b1 and standard error of the slope, and the fact that the t multiplier for 95% confidence and 2 degrees of freedom is 4.3, to construct an approximate 95% confidence interval for the population slope b1, and fill in the blanks: If one rainbow trout has 1 more mg/kg of lead than another, we predict its zinc content to be higher by ______ to ______ mg/kg. (Round to the nearest tenth.)
h. For largescale suckers, use the sample slope b1 and standard error of the slope, and the fact that the t multiplier for 95% confidence and 2 degrees of freedom is 4.3, to construct an approximate 95% confidence interval for the population slope b1, and fill in the blanks: If one largescale sucker has 1 more mg/kg of lead than another, we predict its zinc content to be higher by ______ to ______ mg/kg. (Round to the nearest tenth.)
i. Which of your two confidence intervals contains zero? Explain how this is consistent with the results of your hypothesis tests in parts (b) and (d).
j. Suppose we wanted to use the data to set up a confidence interval to estimate the difference in mean lead contents for rainbow trout minus largescale suckers. Would the appropriate procedure be paired t, two-sample t, several-sample F, chi-square, or regression?
k. Suppose we wanted to use the data to set up a confidence interval to estimate the mean difference in lead and zinc contents for rainbow trout. Would the appropriate procedure be paired t, two-sample t, several-sample F, chi-square, or regression?