How many degrees of freedom are there in the contingency table? The following fi

Question

How many degrees of freedom are there in the contingency table? The following figures was made by local retail merchandisers to determine the relation between weekly advertising expenditures and domestic sales. The following data were recorded. Calculate the correlation coefficient (r_s) using spearman Rank Coefficient, to measure the degree of relation between the two variables. Based from the value of r_s, discuss the significant relationship. Test at alpha =.05 Retail Stores Advertising Cost (BD) Domestic Sales(BD). A 40 385 B 20 400 C 25 395 D 20 365 E 30 475 F 50 440 G 40 490 H 20 420 I 50 560 J 40 525 K 25 480 L 50 510 The following data was made by the machine parts quality control department (MPQCD) of a company regarding the number of defective bolts of two different types of machines (1 & 2) on consecutive days. Two machines have same total output per day. Test that then is no difference between, the two machines or samples come from the same population. Calculate the correlation coefficient using Pearson Product Moment Correlation to measure the degree of relationship between the two operating machines. Based from the value of r_p discuss the significant relationship. Test at alpha =.05

Explanation / Answer

Write the following code to take the data in R and calculate corre;tion coefficient and test for correlation coefficient

Code:

adv_cost<-c(40,20,25,20,30,50,40,20,50,40,25,50)
dom_sales<-c(385,400,395,365,475,440,490,420,560,525,480,510)

cor(adv_cost,dom_sales,method="pearson")

cor.test(adv_cost,dom_sales,
alternative = "greater",
method = "pearson",
exact = NULL, conf.level = 0.95, continuity = FALSE)

Output:

> adv_cost<-c(40,20,25,20,30,50,40,20,50,40,25,50)
> dom_sales<-c(385,400,395,365,475,440,490,420,560,525,480,510)
>
> cor(adv_cost,dom_sales,method="pearson")
[1] 0.6348373
> cor(adv_cost,dom_sales,method="spearman")
[1] 0.633445
>
> cor.test(adv_cost,dom_sales,
+ alternative = "greater",
+ method = "pearson",
+ exact = NULL, conf.level = 0.95, continuity = FALSE)

Pearson's product-moment correlation

data: adv_cost and dom_sales
t = 2.5983, df = 10, p-value = 0.01329
alternative hypothesis: true correlation is greater than 0
95 percent confidence interval:
0.1985218 1.0000000
sample estimates:
cor
0.6348373

So the product moment correlation coefficient = 0.6348373 and rank correlation coefficient = 0.633445

Test Conclusion:

As the p-value of the right tailed test = 0.01329 < 0.05 so at 5% level of significance we can conclude that there is a significant linear relationship between advertising cost and domestic sales

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