Question

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9. Data was analyzed on the shear strength (in kN/mm) and weld diameters (in mm) for a sample of spot welds. Intercept Diameter Coefficients -67.69 28.94 Standard Error 15.19 2.96 t Stat -4.46 9.78 p-value 0.0021 1.002E-05 Lower 95% -102.71 22.12 Upper 95% -32.67 35.76 The explanatory variable is a. (2pts) The response variable is O diameter, shear strength O shear strength, diameter b. (2pts) What hypotheses are being tested with the p-value=1.002E-05? (In other words, what are the hypotheses to test for a linear relationship between shear strength and weld diameter?) O Ho:B1 = 0 versus Ha:B1 < 0 O H.:B1 = 0 versus Ha:B1 > 0 O H.:B1 = 0 versus Ha:B1 = 0 c. (2pts) State the conclusion in terms of the problem. (First, make a decision using the 0.05 significance level.) o There is enough evidence to conclude the true mean shear strength is linearly related to weld diameter. The data indicate that as weld diameter increases, so does shear strength on average. o There is not enough evidence to conclude the true mean shear strength is linearly related to weld diameter. O There is enough evidence to conclude the true mean shear strength is not linearly related to weld diameter. d. (2pts) The 95% CI for B1 = (22.12, 35.76). Interpret the 95% confidence interval for B1 in terms of the problem. o We are 95% confident that the true mean shear strength increases by between 22.12 and 35.76 kN/mm for each one millimeter increase in weld diameter. We are 95% confident that the sample mean shear strength increases by between 22.12 and 35.76 kN/mm for each one millimeter increase in weld diameter. We are 95% confident that the true mean shear strength increases by one unit for each 22.12 and 35.76 mm increase in weld diameter. We are 95% confident that the sample mean shear strength increases by one unit for each 22.12 and 35.76 millimeter increase in weld diameter.

Answer 1

a) Response variable= sheer strength

Explanatory variable= Diameter

b) H₀: Beta₁= 0

H₁: Beta₁ not= 0

c) There is enough evidence to conclude that the mean shear strength is linearly related to weld diameter. The data indicate that as weld diameter increases , so does shear strength on average

d) We are 95% confident that the true mean shear strength increases by between 22.12 and 35.76 kN/mm for each one millimeter increase in weld diameter.