Question

Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars). Determine if there is a significant positive linear correlation between advertising cost and profit. Use a significance level of 0.06 and round all values to 4 decimal places.

Advertising Cost	Profit
3	17
4	24
5	25
6	18
7	29
8	23
9	28
10	34
11	35

R vector x values: 3,4,5,6,7,8,9,10,11
R vector y values: 17,24,25,18,29,23,28,34,35

x-value

y-value

Ho: ρ ≤ 0
Ha: ρ > 0

Find the Linear Correlation Coefficient
r =    (Round to 2 decimal places)

Find the p-value
p-value =    (Round to 4 decimal places)

The p-value is
Select an answer Less than (or equal to) alpha Greater than alpha

The p-value leads to a decision to
Select an answer Reject Ho Do Not Reject Ho Accept Ho

The conclusion is
Select an answer At the 6% significance level, the data provides a significant negative linear correlation between advertising expense and profit. At the 6% significance level, the data provides an insufficient evidence to make a conclusion about the linear correlation between advertising expense and profit. At the 6% significance level, the data provides a significant positive linear correlation between advertising expense and profit. At the 6% significance level, the data provides a significant linear correlation between advertising expense and profit.

Answer 1

I am including the R code as well as the output below and further answering all the questions

> x=c(3,4,5,6,7,8,9,10,11)
> y=c(17,24,25,18,29,23,28,34,35)
> cor(x,y)
[1] 0.8195007
> cor.test(x,y,"greater")

        Pearson's product-moment correlation

data:  x and y
t = 3.7834, df = 7, p-value = 0.003431
alternative hypothesis: true correlation is greater than 0
95 percent confidence interval:
 0.4492709 1.0000000
sample estimates:
      cor 
0.8195007 

Hence

r=0.82

p-value=0.0034

The p-value is

Less than or equal to alpha

The p-value leads to a conclusion to

Reject Ho.

The conclusion is

At the 6% significance level, the data provides a significant positive linear correlation between advertising expense and profit.

Do comment if you have any doubt.

Thank you !!