You may need to use the appropriate appendix table or technology to answer this question.The following data are product weights for the same items produced on two different production lines.Line 1Line 213.613.713.814.114.014.213.914.013.414.613.213.513.314.413.614.812.914.514.414.3 15.0 14.9Test for a difference between the product weights for the two lines. Use ? = 0.05.State the null and alternative hypotheses.H0: Median for line 1 − Median for line 2 < 0Ha: Median for line 1 − Median for line 2 = 0H0: The two populations of product weights are not identical.Ha: The two populations of product weights are identical. H0: Median for line 1 − Median for line 2 ≤ 0Ha: Median for line 1 − Median for line 2 > 0H0: Median for line 1 − Median for line 2 ≥ 0Ha: Median for line 1 − Median for line 2 < 0H0: The two populations of product weights are identical.Ha: The two populations of product weights are not identical.Find the value of the test statistic.W = Find the p-value. (Round your answer to four decimal places.)p-value =

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Description: You may need to use the appropriate appendix table or technology to answer this question.The following data are product weights for the same items produced on two different production lines.Line 1Line 213.613.713.814.114.014.213.914.013.414.613.213.5

a) Null hypothesis: H0: The two populations of product weights are identical. Alternate hypothesis: Ha: The two populations of product weights are not identical. The level of significance is 0.05. Use the given data to form the excel table: Line 1 Rank for Line 1 Line 2 Rank for Line 2 13.6 6.5 13.7 8 13.8 9 14.1 13 14 11.5 14.2 14 13.9 10 14 11.5 13.4 4 14.6 19 13.2 2 13.5 5 13.3 3 14.4 16.5 13.6 6.5 14.8 20 12.9 1 14.5 18 14.4 16.5 14.3 15 15 22 14.9 21 Sum 136.1 70 172 183 Mean 13.61 7 14.33333333 15.25 b) Determine the test statistics using the table. R1=70R2=183W=Sum of ranks for smaller sample size=R1=70μR=n1n1+n2+12=1010+12+12=115σR=n1n2n1+n2+112=10×1210+12+112≈15.1658 z=W-μRσR=70-11515.1658≈-2.9672c) Since we have a two tailed test, the P-value is the probability that the z-score is less than -2.9672 or greater than 2.9672. P-value = P(z < - 2.9672) + P(z > 2.9672) P-value = 2*P(z < - 2.9672) Use excel formula, "=NORM.S.DIST(-2.9672,TRUE)" to determine the P-value. P-value = 2(0.0015) Thus, the P-value = 0.0030. From the above test we have sufficient evidence in the favor of the claim that the two populations of product weights are not identical.

Answered: The following data are product weights…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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You may need to use the appropriate appendix table or technology to answer this question.

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

Line 1	Line 2
13.6	13.7
13.8	14.1
14.0	14.2
13.9	14.0
13.4	14.6
13.2	13.5
13.3	14.4
13.6	14.8
12.9	14.5
14.4	14.3
	15.0
	14.9

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

State the null and alternative hypotheses.

H₀: Median for line 1 − Median for line 2 < 0
H_a: Median for line 1 − Median for line 2 = 0H₀: The two populations of product weights are not identical.
H_a: The two populations of product weights are identical. H₀: Median for line 1 − Median for line 2 ≤ 0
H_a: Median for line 1 − Median for line 2 > 0H₀: Median for line 1 − Median for line 2 ≥ 0
H_a: Median for line 1 − Median for line 2 < 0H₀: The two populations of product weights are identical.
H_a: The two populations of product weights are not identical.

Find the value of the test statistic.

W =

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

p-value =

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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