A shop manager paid a local radio station to air a sales advertisement for one w

Question

A shop manager paid a local radio station to air a sales advertisement for one weekend Since they are charged different fees, there was a variation in the number of times the advertisement was aired. After that sales weekend, the sales manager wants to find out whether there is any association between the number of times the sales advertisement was aired at local radio stations and the sales figures in that weekend The following table gives the data set. Let the random variable X be the number of airings and the random variable Y be the sales in thousands.

Explanation / Answer

Solution:

Here, we have to check whether there is any significant association or correlation exists between the given two variables or not.

Null hypothesis: H0: There is no any significant association between number of airings and sales.

Alternative hypothesis: Ha: There is a significant association between number of airings and sales.

H0: = 0 versus Ha: 0

We are given

Correlation coefficient = r = 0.913082

Sample size = n = 5

Degrees of freedom = n - 2 = 5 – 2 = 3

We assume level of significance or alpha value as 0.05.

The test statistic formula is given as below:

Test statistic = t = r*sqrt[(n – 2)/(1 – r^2)]

Test statistic = t = 0.913082*sqrt[(5 – 2)/(1 – 0.913082^2)]

Test statistic = t = 3.878366

P-value = 0.030357

P-value < alpha value

So, we reject the null hypothesis that there is no any significant association between number of airings and sales.

This means we conclude that there is sufficient evidence that there is a significant association exists between the two variables number of airings and sales in thousands.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.