Concept explainers
The accompanying data on y = ammonium concentration (mg/L) and x = transpiration (ml/h) was read from a graph in the article “Response of Ammonium Removal to Growth and Transpiration of Juncus effusus During the Treatment of Artificial Sewage in Laboratory-Scale Wetlands” (Water Research, 2013: 4265–4273). The article’s abstract stated “a
x | 5.8 | 8.8 | 11.0 | 13.6 | 18.5 | 21.0 | 23.7 |
y | 7.8 | 8.2 | 6.9 | 5.3 | 4.7 | 4.9 | 4.3 |
x | 26.0 | 28.3 | 31.9 | 36.5 | 38.2 | 40.4 |
y | 2.7 | 2.8 | 1.8 | 1.9 | 1.1 | .4 |
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Probability and Statistics for Engineering and the Sciences
- Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using α=0.01. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals?arrow_forwardListed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using α=0.05. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals? Overhead Width 7.1 7.6 9.6 9.2 8.7 8.2 Weight 113 173 242 192 200 188 PLOTS INSERTED AS PICTURE The linear correlation coefficient is r=________. (Round to three decimal places as needed.) The critical values are r=________. (Round to three decimal places as needed. Use a comma to separate answers as needed.) Because the absolute value of the linear correlation coefficient is ▼ less greater than the positive critical value, there ▼ is not is sufficient evidence to support the claim that there is a…arrow_forwardThe authors of this study report a Pearson correlation coefficient estimate of r = 0.23 with a p-value of <0.01. Interpret.arrow_forward
- Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using α=0.01. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals? Overhead Width 7.1 7.7 9.7 9.4 8.7 8.3 Weight 111 201 242 204 197 192 Construct a scatterplot. Choose the correct graph below. The linear correlation coefficient is r=enter your response here. (Round to three decimal places as needed.) The critical values are r=enter your response here. (Round to three decimal places as needed. Use a comma to separate answers as needed.)arrow_forwardA study reports data on the effects of the drug tamoxifen on change in the level of cortisol-binding globulin (CBG) of patients during treatment. With age = x and ΔCBG = y, summary values are n = 26, Σxi = 1619, Σ(xi − x)2 = 3756.96, Σyi = 281.9, Σ(yi − y)2 = 465.34, and Σxiyi = 16,723. (a) Compute a 90% CI for the true correlation coefficient ?. (Round your answers to four decimal places.) , (b) Test H0: ? = −0.5 versus Ha: ? < −0.5 at level 0.05. Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) z = P-value = State the conclusion in the problem context. Reject H0. There is no evidence that ? < −0.5. Reject H0. There is evidence that ? < −0.5. Fail to reject H0. There is evidence that ? < −0.5. Fail to reject H0. There is no evidence that ? < −0.5. (c) In a regression analysis of y on x, what proportion of variation in change of…arrow_forwardDetermine the critical values of r and if it represents a significant linear correlation.arrow_forward
- Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using α=0.01. Overhead width overhead weight 7.1 111 7.6 164 9.8 250 9.2 192 8.8 205 8.2 183 Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals? The linear correlation coefficient is r=? (Round to three decimal places as needed.) The linear correlation coefficient is r=? (Round to three decimal places as needed.) The critical values are r=? (Round to three decimal places as needed. Use a comma to separate answers as needed.) Because the absolute value of the linear correlation coefficient is ______ than the positive critical value, there _______ sufficient evidence to support the claim that there is a linear…arrow_forwardListed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using α=0.01. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals? Overhead Width 7.1 7.6 9.7 9.4 8.8 8.2 Weight 111 198 246 204 202 185 Construct a scatterplot. Choose the correct graph below. (inserted as picture) The linear correlation coefficient is r=__________ (Round to three decimal places as needed.) The critical values are r= (_______,________) (Round to three decimal places as needed. Use a comma to separate answers as needed.) Because the absolute value of the linear correlation coefficient is (greater,less than, equal to) than the positive…arrow_forwardListed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using α=0.05. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals? Overhead Width 7.1 7.6 9.8 9.3 8.8 8.2 Weight 113 165 248 200 202 186 Click here to view a table of critical values for the correlation coefficient. LOADING... Construct a scatterplot. Choose the correct graph below. A. 710100300width (cm)weight (kg) A scatterplot has a horizontal scale labeled “width in centimeters” from 7 to 10 in increments of 0.5 and a vertical scale labeled “weight in kilograms” from 100 to 300 in increments of 20. Six plotted points follow the pattern of a line rising…arrow_forward
- Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using α=0.05. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals? Overhead Width 7.1 7.7 9.8 9.2 8.7 8.3 Weight 112 204 245 194 198 187 1. Construct a scatterplot graph 2. The linear correlation coefficient r is 3. The critical values are r= 4. Because the absolute value of the linear correlation coefficient is_____than the positive critical value, there___sufficient evidence to support the claim that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals for a significance level of α=0.05.arrow_forwardThe accompanying data represent the number of days absent, x, and the final exam score, y, for a sample of college students in a general education course at a large state university. No. of absences, x 0 1 2 3 4 5 6 7 8 9 Final exam score, y 89.7 86.1 83.6 81.8 78.7 74.1 64.4 71.2 64.5 66.4 REFERENCE Critical Values for Correlation Coefficient n 3 0.997 4 0.950 5 0.878 6 0.811 7 0.754 8 0.707 9 0.666 10 0.632 11 0.602 12 0.576 13 0.553 14 0.532 15 0.514 16 0.497 17 0.482 18 0.468 19 0.456 20 0.444 21 0.433 22 0.423 23 0.413 24 0.404 25 0.396 26 0.388 27 0.381 28 0.374 29 0.367 30 0.361 n (a) Find the least-squares regression line treating number of absences as the explanatory variable and the final exam score as the response variable. y hat = _____x + _____ Round to 3 decimal…arrow_forwardListed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using α=0.05. Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals? Overhead Width 7.1 7.8 9.8 9.3 8.7 8.3 Weight 113 211 246 198 201 190 The linear correlation coefficient is r=enter your response here. (Round to three decimal places as needed.) The critical values are r=enter your response here. (Round to three decimal places as needed. Use a comma to separate answers as needed.)arrow_forward
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