  # 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 0.05 and round all values to 4 decimal places.Advertising CostProfit323420527625730823921102311331229Find p value.

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 0.05 and round all values to 4 decimal places.

3 23
4 20
5 27
6 25
7 30
8 23
9 21
10 23
11 33
12 29

Find p value.

check_circleExpert Solution
Step 1

Let r denote the linear correlation between advertising cost (x) and profit (y). The hypotheses are given below:

Null hypothesis:

H0 : r = 0

That is, the sample correlation coefficient (r) is not significantly different from zero. There is no significant positive linear relationship between advertising cost and profit.

Alternative hypothesis:

Ha : r ≠ 0

That is, the sample correlation coefficient is significantly different from zero.

There is a significant positive linear relationship between advertising cost and profit.

Step 2

Degrees of freedom:

The formula for degrees of freedom is as follows:

Df = n – 2.

The number of data values given are 10, that is n = 10.

Substitute n = 10 in the degrees of freedom formula.

Df = n – 2 = 10 – 2 = 8.

The level of significance for the test is 0.05.

Step 3

Sample correlation coefficient:

The value of the sample correlation coefficient (r) can be obtained using Excel formula.

Enter the values of advertising cost in columns A2:A11 in Excel.

Enter the values...

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