Question

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

Time (minutes)   Mass (Pounds)
0   6.59
2   6.09
4   5.43
6   4.87
8   4.41
10   4.05
12   3.57
14   3.14
16   2.81
18   2.45
20   2.22
25   1.49
30   1.02
45   0.14
60   0.00

a. Find a 90​% confidence interval for the mean mass of all spills with an elapsed time of 32 minutes. Interpret the result.

What is the confidence​ interval?

left parenthesis nothing comma nothing right parenthesis,

​(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 the mean mass of the spill before 32 minutes has passed.

B.We are 90​% confident that the interval will not contain the mean mass of the spill at 32 minutes.

C.We are 90​% confident that the interval will contain the mean mass of the spill after 32 minutes.

D.We are 90​% confident that the interval will contain 32 minutes.

b. Find a 90​% prediction interval for the mass of a single spill with an elapsed time of 32 minutes. Interpret the result.

What is the prediction​ interval?

(nothing),(nothing ),

​(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 the mass of the spill after 32 minutes.

B.We are 90​%confident that the interval will not contain the mass of the spill after 32 minutes.

C.We are 90​% confident that the interval will contain the mass of the spill before 32 minutes has passed.

D.We are 90​% confident that the interval will contain 32 minutes.

c. Compare the​ intervals, parts a and b. Which interval is​ wider? Will this always be the​ case? Explain. Fill in the blanks below.

The

▼

prediction

confidence interval is wider.

This

▼

will not

will always be the case because the error of this interval is

▼

the sum of two errors.

random error.

twice the error of the other interval.

half the error of the other interval.

Answer 1

The statistical software output for this problem is:

Hence,

a) 90% confidence interval:

(1.111, 2.140)

We are 90​% confident that the interval will contain the mean mass of the spill after 32 minutes.

b) 90% prediction interval:

(0.041, 3.211)

We are 90​% confident that the interval will contain the mass of the spill after 32 minutes.

c) Prediction; will always be the case; the sum of two errors