A sample of 40 women is obtained and their heights (in inches) and pulse rates (in beats per minute) are measured. The linear correlation coefficient is 0.251 and the equation of the regression line is y=18.3 + 0.880x where x represents height. The mean of 40 heights is 62.8 in and the mean of the 40 pulse rates is 77.3 beats per minute. Find the best predicted pulse rate of a women who is 71 in tall. Use a significance level of α=0.01.
The equation of the regression line is given. In order to determine if the regression line is good enough to be used, we perform a hypothesis test. There are two methods of performing a hypothesis test for this question. Both methods will be presented.
Hypothesis Test Method #1
Step 1) Write the hypothesis statements (2-tailed test)
H0: ρ = 0
H1: ρ ≠ 0
Step 2) Write the absolute value of the linear correlation coefficient that is given.
|r| = |0.251| = 0.251
Step 3) Look up the appropriate critical value in a table of Critical Values of the Pearson Correlation Coefficient r.
Note) Some tables use n, the number of women tested.
Some tables use ...
This solution provides a step-by-step explanations of how to use the information given on heights and pulse rates. It discusses 2 different methods of testing the information to arrive at the same conclusion. 477 words, formulas, computations and a table.