Data on the rate at which a volatile liquid will spread across a surface are in

Question

Data on the rate at which a volatile liquid will spread across a surface are in the table. Complete parts a through

Find a 95% confidence interval for the mean mass of all spills with an elapsed time of 4 minutes. Interpret the result.

What is the confidence interval?

Round to three decimals  

We are 95% confident that the interval will not contain the mean mass of the spill at 4 minutes.

B.

We are 95%

confident that the interval will contain the mean mass of the spill before 4minutes has passed.

C.

We are 95% confident that the interval will contain 4minutes.

D.

We are 95% confident that the interval will contain the mean mass of the spill after 4 minutes

b

Find a 95%prediction interval for the mass of a single spill with an elapsed time of 4 minutes. Interpret the result.

What is the prediction interval

Round three decimal places

We are 95% confident that the interval will not contain the mass of the spill after 4 minutes.

B.

We are 95% confident that the interval will contain the mass of the spill before 4 minutes has passed.

C.

We are 95% confident that the interval will contain 4 minutes.

D.

We are 95% confident that the interval will contain the mass of the spill after 4 minutes

Compare the intervals, parts a and

b.

The

prediction

confidence

interval is wider. This

will

will not

always be the case because the error of this interval Which interval is wider? Will this always be the case? Explain. Fill in the blanks below.

Time (minutes) Mass (Pounds) 0 6.72 2 6.05 4 5.49 6 4.88 8 4.46 10 3.88 12 3.58 14 3.17 16 2.85 18 2.45 20 2.22 25 1.54 30 0.94 45 0.21 60 0

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Mass (Pounds)
Independent Variable: Time (minutes)
Mass (Pounds) = 5.2808164 - 0.11397128 Time (minutes)
Sample size: 15
R (correlation coefficient) = -0.91478088
R-sq = 0.83682406
Estimate of error standard deviation: 0.86384161

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

95% confidence interval: (4.184, 5.466)

We are 95% confident that the interval will contain the mean mass of the spill after 4 minutes

95% prediction interval: (2.852, 6.798)

We are 95% confident that the interval will contain the mass of the spill after 4 minutes

The prediction interval is wider. This will always be the case because the error of this interval Which interval is wider

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 5.2808164 0.33596883 0 13 15.718173 <0.0001 Slope -0.11397128 0.013958371 0 13 -8.1650847 <0.0001

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