pan's high population density has resulted in a multitude of resource-usage problems. One especially serious difficulty concerns waste removal. An article reported the development of a new compression machine for processing sewage sludge. An important part of the investigation involved relating the moisture content of compressed pellets (y, in %) to the machine's filtration rate (x, in kg-DS/m/hr). The following data was read from a graph in the article. x 125.8 98.1 201.4 147.3 145.9 124.7 112.2 120.2 161.2 178.9 159.5 145.8 75.1 151.5 144.2 125.0 198.8 133.9 y 77.9 76.8 81.5 79.8 78.2 78.3 77.5 77.0 80.1 80.2 79.9 79.0 76.9 78.2 79.5 78.1 81.5 71.0 (a) Determine the slope and intercept of the estimated regression line. (Round your answers to 5 decimal places, if needed.) slope: intercept: (b) Does there appear to be a useful linear relationship? Carry out a test using the ANOVA approach and a significance level of 0.05. State the appropriate null and alternative hypotheses. H0: β1 = 0 vs. HA: β1 > 0 H0: β1 ≠ 0 vs. HA: β1 = 0 H0: β1 = 0 vs. HA: β1 ≠ 0 H0: β1 = 0 vs. HA: β1 < 0 The test statistic is F0 = . (Round your answer to 3 decimal places, if needed.) Using the appropriate statistical table, the p-value range is . Based on the p-value, the null hypothesis. This data sufficient evidence to conclude that the slope is zero. (c) Does there appear to be a useful linear relationship? Carry out a test using the t-test approach and a significance level of 0.05. State the appropriate null and alternative hypotheses. H0: β1 = 0 vs. HA: β1 < 0 H0: β1 ≠ 0 vs. HA: β1 = 0 H0: β1 = 0 vs. HA: β1 ≠ 0 H0: β1 = 0 vs. HA: β1 > 0 The test statistic is t0 = . (Round your answer to 3 decimal places, if needed.) Using the appropriate statistical table, the p-value range is . Based on the p-value, the null hypothesis. This data sufficient evidence to conclude that the slope is zero.
pan's high population density has resulted in a multitude of resource-usage problems. One especially serious difficulty concerns waste removal. An article reported the development of a new compression machine for processing sewage sludge. An important part of the investigation involved relating the moisture content of compressed pellets (y, in %) to the machine's filtration rate (x, in kg-DS/m/hr). The following data was read from a graph in the article.
| x | 125.8 | 98.1 | 201.4 | 147.3 | 145.9 | 124.7 | 112.2 | 120.2 | 161.2 | 178.9 | 159.5 | 145.8 | 75.1 | 151.5 | 144.2 | 125.0 | 198.8 | 133.9 |
| y | 77.9 | 76.8 | 81.5 | 79.8 | 78.2 | 78.3 | 77.5 | 77.0 | 80.1 | 80.2 | 79.9 | 79.0 | 76.9 | 78.2 | 79.5 | 78.1 | 81.5 | 71.0 |
(a) Determine the slope and intercept of the estimated regression line. (Round your answers to 5 decimal places, if needed.)
slope:
intercept:
(b) Does there appear to be a useful linear relationship? Carry out a test using the ANOVA approach and a significance level of 0.05. State the appropriate null and alternative hypotheses.
The test statistic is F0 = . (Round your answer to 3 decimal places, if needed.)
Using the appropriate statistical table, the p-value
Based on the p-value, the null hypothesis. This data sufficient evidence to conclude that the slope is zero.
(c) Does there appear to be a useful linear relationship? Carry out a test using the t-test approach and a significance level of 0.05. State the appropriate null and alternative hypotheses.
The test statistic is t0 = . (Round your answer to 3 decimal places, if needed.)
Using the appropriate statistical table, the p-value range is .
Based on the p-value, the null hypothesis. This data sufficient evidence to conclude that the slope is zero.
(d) The conclusions of the tests were since we know the following relationship between t0 and F0.
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