a. Find a 90% confidence interval for the mean mass of all spills with an elapse

Question

a. Find a 90% confidence interval for the mean mass of all spills with an elapsed time of 41 minutes. Interpret the result What is the confidence interval? Round to three decimal places as needed ) Interpret the result. Choose the correct answer below. A. We are 90% confident that the interval will contain 41 minutes. 0 B. We are 90% confident that the interval will not contain the mean mass of the spill at 41 minutes. O c. we are 90% confident that the interval will contain the mean mass of the spill before 41 minutes has passed We are 90% confident that the interval will contain the mean mass of the spill after 41 minutes. 0 D. b. Find a 90% prediction interval for the mass of a single spill with an elapsed time of 41 minutes. Interpret the result. What is the prediction interval? Show all

Explanation / Answer

Result:

90% confidence interval =(-0.096, 1.290).

Interpretation: option D

90% prediction interval =(-1.083, 2.278)

Interpretation: option B

The prediction interval is wide, this will always true because sum of two errors.

Regression Analysis

r²

0.836

n

15

r

-0.915

k

1

Std. Error

0.865

Dep. Var.

mass

ANOVA table

Source

SS

df

MS

F

p-value

Regression

49.7040

1  

49.7040

66.50

1.81E-06

Residual

9.7169

13  

0.7475

Total

59.4209

14  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=13)

p-value

90% lower

90% upper

Intercept

5.2679

0.3362

15.667

8.06E-10

4.6724

5.8633

time

-0.1139

0.0140

-8.155

1.81E-06

-0.1387

-0.0892

Predicted values for: mass

90% Confidence Interval

90% Prediction Interval

time

Predicted

lower

upper

lower

upper

Leverage

41

0.59719

-0.09566

1.29005

-1.08334

2.27773

0.205

Regression Analysis

r²

0.836

n

15

r

-0.915

k

1

Std. Error

0.865

Dep. Var.

mass

ANOVA table

Source

SS

df

MS

F

p-value

Regression

49.7040

1  

49.7040

66.50

1.81E-06

Residual

9.7169

13  

0.7475

Total

59.4209

14  

Regression output

confidence interval

variables

coefficients

std. error

   t (df=13)

p-value

90% lower

90% upper

Intercept

5.2679

0.3362

15.667

8.06E-10

4.6724

5.8633

time

-0.1139

0.0140

-8.155

1.81E-06

-0.1387

-0.0892

Predicted values for: mass

90% Confidence Interval

90% Prediction Interval

time

Predicted

lower

upper

lower

upper

Leverage

41

0.59719

-0.09566

1.29005

-1.08334

2.27773

0.205

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