[confidence intervals] following information is from a report on the determinati

Question

[confidence intervals]

following information is from a report on the determination of silver content of galena crystals grown in a closed hydrothermal system over a range of temperature. With x = crystallization temperature in °C and y = Ag2S in mol%, the data follows.

(a) Estimate true average silver content when temperature is 683°C using a 95% confidence interval. (Give answers accurate to 3 decimal places.)
( ,  )

(b) Calculate a 95% CI for the true average change in silver content associated with a 1°C increase in temperature. (Give answers accurate to 5 decimal places.)

x   398 292 352 575 568 450 550 408 484 344 509 594 594 y     0.1   0.05   0.23   0.43   0.21   0.40   0.44   0.44   0.45   0.09   0.59   0.63   0.60

Explanation / Answer

model => y = -0.327 + 0.00146x

Therefore, at x = 683, y = -0.327 + 0.00146*683 = 0.67894

Now, constructing a 95% confidence interval

(0.67894-t*s, 0.67894+t*s), now for 95%, t for degrees of freedom = n-2 = 13-2 = 11 is 2.201

assuming given s = 0.138 is the standard error for the regression

=> 95% CI => (0.67894-2.201*0.138, 0.67894+2.201*0.138)

=> (0.375, 0.983)

b) 95% CI for change in silver content for 1C increase in temperture = 95% CI for delta1

=> standard error for beta = standard error for regression = s = 0.138

=> 95% CI = (delta1 - t*s, delta1 + t*s), the value of t will be same as above = 2.201

=> (0.00146 - 2.201*0.138, 0.00146 + 2.201*0.138)

=> (-0.30228, 0.30520)

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