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A quality control engineer developed a control chart to maintain the weights of family size ketchup...

A quality control engineer developed a control chart to maintain the weights of family size ketchup bottle (desired populatio

A quality control engineer developed a control chart to maintain the weights of family size ketchup bottle (desired population median weight is 68 oz). Weights (in ounces) of 16 bottles taken at randomly selected times from the production process are as follows (data displayed in order of time of the selection): 68.2, 71.6, 69.3, 71.6,70.4, 65, 63.6, 64.7,65.3, 64.2, 67.6, 68.6, 66.8,67.9, 66.7,70.1 (a) (3 points) Do the data provide any evidence to conclude that the sample is not a random sample? Use a=0.05. Include the R function used, report the p-value and write your conclusion. 68 oz. Use alpha = 0.05. Include the R function used, p-value, and write your (b) (3 points) Do Wilcoxon signed-rank test to see if the median score of the sampled population is less than conclusion. (c) (2 points) What assumptions are necessary for the validity of the test in step (b)? Answer the above questions in the order displayed above.
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A] We use run test to conclude that data points are random or not .

We use library randtest in R to compute run test So make sure you install it by downloding from cran or use command install.packages("randtest") to install it.

R scipt for run test:

x=c(68.2,71.6,69.3,71.6,70.4,65,63.6,64.7,65.3,64.2,67.6,68.6,66.8,67.9,66.7,70.1)
library(randtests)
runs.test(x,alternative = "two.sided")

Out put: statistic = -1.0351, runs = 7, n1 = 8, n2 = 8, n = 16, p-value = 0.3006 alternative hypothesis: nonrandomness

Conclusion: Here p value of run test statistics is 0.3006 which is > alpha=0.05. So we accept null hypothesis that is sample are randoms. ( i.e there is no evidance that sample are not random )

B] Wilcoxon signed -rank test to test wheather median score of sample population is less than 68oz.

R script for wilcoxon singed- rank test:

x=c(68.2,71.6,69.3,71.6,70.4,65,63.6,64.7,65.3,64.2,67.6,68.6,66.8,67.9,66.7,70.1)
library(stats)
wilcox.test(x=1:100, mu = 68,alternative = "greater")
Out put: V = 56.5, p-value = 0.7326 alternative hypothesis: true location is greater than 68

Conclusion: Here p value of wilcoxon singed rank test is 0.7326 so we accept null hypothesis that sample population median is less than 68.

C] Following assumption are necessary for wilcoxon singed test used in B]

this test does not required normality assumption only assumption required is randomness in sample.  

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