When survey data indicated that a coffee company needed to improve its package-s
ID: 3045226 • Letter: W
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.
Bag Plate gap (X) Tear rating (Y)
1 0.3 0.06
2 0.00 0.07
3 1.50 0.43
4 1.50 0.88
5 0.00 0.33
6 -0.30 0.32
7 0.00 0.78
8 0.30 1.92
9 -0.30 0.26
10 -2.10 0.14
11 -2.10 0.14
12 2.40 3.71
13 -2.10 0.02
14 0.30 0.58
15 -3.00 0.01
16 -2.10 0.12
17 1.80 0.47
18 2.10 4.22
19 0.00 0.05
Construct a 90 % confidence interval estimate of the mean tear rating for all bags of coffee when the plate gap is 0.
___ Y|X=0 ___
(Type integers or decimals. Round to three decimal places as needed. Use ascending order.)
Explanation / Answer
The statistical software output for this problem is:
Simple linear regression results:
Dependent Variable: Y
Independent Variable: X
Y = 0.80940194 + 0.48257608 X
Sample size: 19
R (correlation coefficient) = 0.62592851
R-sq = 0.3917865
Estimate of error standard deviation: 0.97639701
Parameter estimates:
Analysis of variance table for regression model:
Predicted values:
Hence,
Required confidence interval:
0.419 Y|X=0 1.200
Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 0.80940194 0.22442647 0 17 3.6065351 0.0022 Slope 0.48257608 0.14582924 0 17 3.3091859 0.0041Related Questions
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