Question

When survey data indicated that a coffee company needed to improve its​ package-sealing process, an experiment was conducted to determine the factors in the​ bag-sealing equipment that might be affecting the ease of opening the bags without tearing the inner liner of the bag. Data were collected on 19 bags and the plate gap on the​ bag-sealing equipment was used to predict the tear rating of a bag. Complete parts​ (a) through ​(b).

Bag   Plate gap (X)   Tear rating (Y)
1   -0.3   0.06
2   -0.30   0.03
3   1.80   0.45
4   1.80   0.88
5   0.00   0.31
6   0.30   0.38
7   -0.30   0.77
8   0.00   1.96
9   -0.30   0.22
10   -1.80   0.19
11   -1.50   0.16
12   3.00   3.79
13   -1.80   0.05
14   0.00   0.57
15   -2.40   0.03
16   -1.80   0.12
17   1.50   0.41
18   1.80   4.02
19   0.00   0.09

a. Construct a 95​% confidence interval estimate of the mean tear rating for all bags of coffee when the plate gap is 0.3

b. Construct a 95​% prediction interval of the tear rating for an individual bag of coffee when the plate gap is 0.3

Answer 1

The statistical software output for this problem is :

(a)

A 95​% confidence interval estimate of the mean is :

(0.4663 , 1.3925)

(b)

A 95​% prediction interval is :

(-1.0955 , 2.9544)