Using the data given in the table below, answer the following questions. (Round

Question

Using the data given in the table below, answer the following questions. (Round your final answers to 3 decimal places.) (a) Use Excel, MegaStat, or MINITAB to calculate the correlation coefficient. (A negative value should be indicated by a minus sign.) r_calc (b) Use Excel or Appendix D to find t .025 for a two-tailed test at alpha = .05. t_.025 plusminus (c) Calculate the t test statistic. (Negative value should be indicated by a minus sign.) t_calc (d) Should we reject the null hypothesis of zero correlation? No Yes

Explanation / Answer

we shall use the open source statistical package R to answer this . Thecomplete Rsnippet is as follows

age<-c(32,49,33,10,36,35,39,27,18,28)
spent<-c(2.84,6.54,1.41,6.22,6.26,6.76,3.54,6.01,8.32,4.39)

#findthe correlation
cor(age,spent)

t.test(age,spent)

The result is

> cor(age,spent)
[1] -0.2428054
> t.test(age,spent)

   Welch Two Sample t-test

data: age and spent
t = 7.2586, df = 9.6752, p-value = 3.258e-05 , as the p value is less than 0.05 , hence we should reject the null hypothesis
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
17.61658 33.32542
sample estimates:
mean of x mean of y
30.700 5.229

we can use the excel function =T.INV(0.025,9) , where 9 is the degree of freedom 10-1 = 9

-2.26216

-2.26216

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