Question

The table below lists the numbers of audience impressions​ (in hundreds of​ millions) listening to songs and the corresponding numbers of albums sold​ (in hundreds of​ thousands). Does it appear that album sales are affected very strongly by the number of audience​ impressions? Use a significance level of α=0.05.

Determine the null and alternative hypotheses for this test.

Determine the correlation coefficient.

Audience Impressions	14	22	28	26	25	27	19	18	28
Albums Sold	10	6	7	5	15	12	16	18	7

Answer 1

(x-x) (y-y) 6.0000 4.6667 -18.3333 -17.0000 8.6667 5.3333 21.3333 -36.6667 -18.3333 87.0000 (x-x) 81.0000 1.0000 25.0000 9.0000 4.0000 16.0000 16.0000 25.0000 25.0000 202.0000 (y-y) 0.4444 21.7778 13.4444 32.1111 18.7778 1.7778 28.4444 53.7778 13.4444 184.0000 S.No 10 2 4 26 25 27 19 18 15 12 16 Total SSY Mean 23.0000 10.6667 SSX null hypothesis Alternate Hypothesis 0 0 for 0.05 level,two tailed test and n-2-7 degree of freedom, critical t- Decision rule: 2.3646 reject Ho if absolute value of test statistic It| >2.365 correlation coefficient rS(Vs"Sy - 0.451 test statistic: -1.3379 p value 0.2228

as test statistic is not in critical region we cannot conclude that album sales are affected very strongly by the number of audience​ impressions