Statistics Chapter 10 Exam Questions with Verified Solutions Latest Update 2024 Already Passed

Statistics Chapter 10 Exam Questions with Verified Solutions Latest Update 2024 Already Passed If we find that there is a linear correlation between the concentration of carbon dioxide in our atmosphere and the global temperature, does that indicate that changes in the concentration of carbon dioxide cause changes in the global temperature? - Answers No. The presence of a linear correlation between two variables does not imply that one of the variables is the cause of the other variable. For a sample of eight bears, researchers measured the distances around the bears' chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is r =0.996 Using α=0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest size? Critical Values for the Coefficient n a=0.05 a=0.01 4 0.950 0.990 5 0.878 0.959 6 0.811 0.917 7 0.754 0.875 8 0.707 0.834 9 0.666 0.798 10 0.632 0.765 11 0.602 0.735 12 0.576 0.708 13 0.553 0.684 14 0.532 0.661 15 0.514 0.641 16 0.497 0.623 17 0.482 0.606 18 0.468 0.590 19 0.456 0.575 20 0.444 0.561 25 0.396 0.505 30 0.361 0.463 35 0.335 0.430 40 0.312 0.402 45 0.294 0.378 50 0.279 0.361 60 0.254 0.330 70 0.236 0.305 80 0.220 0.286 90 0.207 0.269 100 0.196 0.256 NOTE: To test Ho:p=0, against H1:p# 0, reject - Answers A.)Yes, because the absolute value of the test statistic exceeds the critical value of 0.707. B.)What proportion of the variation in weight can be explained by the linear relationship between weight and chest size? 0.996 squared = 0.992 Therefore, 99.2% of the variation in weight can be explained by the linear relationship between weight and chest size. The heights (in inches) and pulse rates (in beats per minute) for a sample of 1919 women were measured. Using technology with the paired height/pulse data, the linear correlation coefficient is found to be 0.501 Is there sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women? Use a significance level of α=0.05 - Answers Because l 0.501 l GREATER than the critical value, there IS sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women for a significance level of α=0.05. The heights (in inches) and pulse rates (in beats per minute) for a sample of 55 women were measured. Using technology with the paired height/pulse data, the linear correlation coefficient is found to be 0.923. Is there sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women? Use a significance level of α=0.01 - Answers Because l 0.923 l is LESS than the critical value, there IS NOT sufficient evidence to support the claim that there is a linear correlation between the heights and pulse rates of women for a significance level of α=0.01 Which of the following is NOT true for a hypothesis test for correlation? A.) If|r|>critical value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.Your answer is correct. B.) If l r l ≤critical value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation. C.) If the P-value is less than or equal to the significance level, we should reject the null hypothesis and conclude that there is sufficient evidence to support the claim of a linear correlation. D.) If the P-value is greater than the significance level, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation. - Answers A.) If |r|>critical value, we should fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim of a linear correlation.