Suppose the following data are product weights for the same items produced on two different production lines. Line 1 Line 2 13.1 13.4 13.9 14.7 14.0 14.6 13.5 14.0 13.3 14.1 13.6 13.2 13.8 14.3 13.1 14.9 12.5 14.2 14.3 14.8 15.0 14.5 A. Test for a difference between the product weights for the two lines. Use α = 0.05. State the null and alternative hypotheses. 1. H0: The two populations of product weights are identical. Ha: The two populations of product weights are not identical. 2. H0: Median for line 1 − Median for line 2 ≤ 0 Ha: Median for line 1 − Median for line 2 > 0 3. H0: Median for line 1 − Median for line 2 < 0 Ha: Median for line 1 − Median for line 2 = 0 4. H0: The two populations of product weights are not identical. Ha: The two populations of product weights are identical. 5. H0: Median for line 1 − Median for line 2 ≥ 0 Ha: Median for line 1 − Median for line 2 < 0 B. Find the value of the test statistic. W = Find the p-value. (Round your answer to four decimal places.) p-value = C. State your conclusion. 1. Reject H0. There is not sufficient evidence to conclude that there is a significant difference between the product weights for the two lines. 2. Do not reject H0. There is sufficient evidence to conclude that there is a significant difference between the product weights for the two lines. 3. Reject H0. There is sufficient evidence to conclude that there is a significant difference between the product weights for the two lines. 4. Do not reject H0. There is not sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose the following data are product weights for the same items produced on two different production lines.

Line 1	Line 2
13.1	13.4
13.9	14.7
14.0	14.6
13.5	14.0
13.3	14.1
13.6	13.2
13.8	14.3
13.1	14.9
12.5	14.2
14.3	14.8
	15.0
	14.5

A. Test for a difference between the product weights for the two lines. Use α = 0.05.

State the null and alternative hypotheses.

1. H₀: The two populations of product weights are identical.
H_a: The two populations of product weights are not identical.

2. H₀: Median for line 1 − Median for line 2 ≤ 0
H_a: Median for line 1 − Median for line 2 > 0

3. H₀: Median for line 1 − Median for line 2 < 0
H_a: Median for line 1 − Median for line 2 = 0

4. H₀: The two populations of product weights are not identical.
H_a: The two populations of product weights are identical.

5. H₀: Median for line 1 − Median for line 2 ≥ 0
H_a: Median for line 1 − Median for line 2 < 0

B. Find the value of the test statistic.

W =

Find the p-value. (Round your answer to four decimal places.)

p-value =

C. State your conclusion.

1. Reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.

2. Do not reject H₀. There is sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.

3. Reject H₀. There is sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.

4. Do not reject H₀. There is not sufficient evidence to conclude that there is a significant difference between the product weights for the two lines.

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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