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 (c). Click the icon to view the data table. a. Construct a 95% confidence interval estimate of the mean tear rating for all bags of coffee when the plate gap is 0.3. ] ≤ HY|X = 0.3 ≤ [ (Type integers or decimals. Round to three decimal places as needed. Use ascending order.)
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 (c). Click the icon to view the data table. a. Construct a 95% confidence interval estimate of the mean tear rating for all bags of coffee when the plate gap is 0.3. ] ≤ HY|X = 0.3 ≤ [ (Type integers or decimals. Round to three decimal places as needed. Use ascending order.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
A. Find the 95% Confidence Interval
B. Find the 95% Prediction Interval
|
Bag
|
Plate gap
(X)
|
Tear rating
(Y)
|
||||
|---|---|---|---|---|---|---|
|
1
|
0
|
|
0.08
|
|
|
|
|
2
|
|
−0.30
|
|
0.04
|
|
|
|
3
|
|
1.80
|
|
0.42
|
|
|
|
4
|
|
2.10
|
|
0.87
|
|
|
|
5
|
|
−0.30
|
|
0.39
|
|
|
|
6
|
|
0.30
|
|
0.34
|
|
|
|
7
|
|
0.00
|
|
0.77
|
|
|
|
8
|
|
0.30
|
|
1.98
|
|
|
|
9
|
|
0.30
|
|
0.25
|
|
|
|
10
|
|
−2.10
|
|
0.11
|
|
|
|
11
|
|
−1.50
|
|
0.13
|
|
|
|
12
|
|
3.00
|
|
3.76
|
|
|
|
13
|
|
−1.80
|
|
0.06
|
|
|
|
14
|
|
0.30
|
|
0.55
|
|
|
|
15
|
|
−2.40
|
|
0.04
|
|
|
|
16
|
|
−1.50
|
|
0.12
|
|
|
|
17
|
|
1.50
|
|
0.42
|
|
|
|
18
|
|
1.80
|
|
4.37
|
|
|
|
19
|
|
−0.30
|
|
0.04
|
|
|
Transcribed Image Text:**Title: Improving Package-Sealing for Coffee Bags: An Experimental Approach**
**Introduction:**
When survey data indicated that a coffee company needed to enhance its package-sealing process, an experiment was devised. The purpose was to identify factors in the bag-sealing equipment that might affect the ease of bag opening without damaging the inner liner. Data were collected on 19 bags, focusing on the plate gap in the sealing equipment as a predictor for the tear rating of a bag.
**Data Collection:**
- **Sample Size:** 19 bags
- **Variable of Interest:** Plate gap on bag-sealing equipment
**Task Overview:**
Complete parts (a) through (c) using the data provided.
**Instructions:**
- Click the icon to view the complete data table.
**Task a: Confidence Interval Construction**
- **Objective:** Construct a 95% confidence interval estimate for the mean tear rating of coffee bags when the plate gap is set at 0.3.
- **Instructions:** Enter integers or decimals rounded to three decimal places as needed. Use ascending order to present your results.
- **Formula:** \( \boxed{\phantom{0}} \leq \mu_{Y|X=0.3} \leq \boxed{\phantom{0}} \)
- **Note:** This will provide an estimate range for the mean tear strength for bags with a specified plate gap setting.
**Conclusion:**
This experiment is critical for optimizing packaging processes to ensure easy handling and maintain the quality of coffee bags.
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VIEWStep 3: Determine the sum of squares, MSE, standard error and critical value for the given data.
VIEWStep 4: Determine the confidence interval estimate of mean tear ratings when the plate gap is 0.30.
VIEWStep 5: Determine the prediction interval estimate of mean tear ratings when the plate gap is 0.30.
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