Problem 3

Contracts in the arts often give more money to the producer during initial weeks; other parties' revenues are based more on sales in later weeks. For instance, the production studio gets most of the box office revenues during initial weeks that a movie is in theatres, while theatres get most of the revenues from later weeks.

The Excel file "Problem3_Country.xlsx" contains sales (in units of number of albums sold) from a random sample of "country" albums and the Excel file "Problem3_Pop.xlsx" contains sales (in units of number of albums sold) from a random sample of "pop" albums. For instance, country album number 4 had sales volume of 30,354 during the first 4 weeks that the album was available. Its sales volume in all the weeks after the first 4 weeks was 395,807.

Assume that the revenues of the recording studio are proportional to the number of albums sold, and that the recording studio gets 100% of albums' revenues during the first 4 weeks and only 50% of revenues thereafter. In other words, for country album number 4, recording studio profits would be

Revenue = k * (30354 + 0.5*395807).

Although we don't know the proportionality constant k, let us assume that it is the same for all albums, let this be $10. In other words, let's just act as if the revenue equation for any album is

Revenue = 10*(S₁ + 0.5*S₂),

where S₁ is sales (number of albums sold) in the first 4 weeks, and S₂ is the sales (number of albums sold) in all the remaining weeks, and "Revenue" is revenue of the recording studio in dollars.

On the first Excel file (Problem3_Country.xlsx) you have S₁ and S₂ for country albums, and on the second Excel file (Problem3_Pop.xlsx) you have S₁ and S₂ for pop albums.

(a) Create new columns that represent the revenue of the recording studio for country albums and pop albums.

Report the mean and median revenue from country albums?

Report the mean and median revenue from pop albums?

(b) Which of the two following situations would lead to a median revenue that is lower than the mean revenue?

(i) The data contains a few albums with unusually high revenues

(ii) The data contains a few albums with unusually low revenues

(c) Calculate and report the correlation between the album sales during the first 4 weeks and the remaining weeks for country albums. Based on this correlation please check/circle all appropriate statementsfrom the following three.

(i) Albums that sell more copies in the first four weeks also tend to sell more copies in the remaining weeks thereafter.

(ii) The sales in the first four weeks and the remaining weeks thereafter have no relation at all.

(iii) Albums that sell fewer copies in the first four weeks also tend to sell fewer copies in the remaining weeks thereafter.

(d) What is the population mean difference across volume sales in the first 4 weeks and volume sales beyond the 4 weeks for country albums?

To answer this you need to generate a 95% confidence interval for the mean difference between the sales volume for first 4 weeks that the album was available and all the weeks after the first 4 weeks.

(e) Interpret the constructed confidence interval in part (d).

Country

Country_Album_No	First_4_Week_Sales	Remaining_Weeks_Sales
1	44220	483467
2	78730	152075
3	55661	603645
4	30354	395807
5	37995	259610
6	130983	99893
7	45024	710679
8	190652	841129
9	32036	975641
10	363005	594372
11	42740	111901
12	71730	175009
13	56717	85954
14	40033	252840
15	63523	739259
16	77272	93429
17	79954	112204
18	295079	1356929
19	33668	58719
20	76955	254315
21	46933	218071
22	107969	617652
23	68496	143769
24	37261	161011
25	64475	393330
26	112145	188968
27	27188	799746
28	33597	255592
29	39825	280690
30	61486	204019
31	381565	1353483
32	408610	1719513
33	74799	165402
34	51875	122214
35	38691	108156
36	449844	879733
37	57156	548361
38	83375	282861
39	142122	541717
40	82665	326235
41	28979	58931
42	37265	985470
43	66219	130110
44	29521	153297
45	34583	150398
46	151447	622228
47	64372	503425
48	28319	128505
49	18393	194666
50	48443	61039
51	109868	215992
52	67257	58213

Pop:

Pop_Album_No	First_4_Week_Sales	Remaining_Weeks_Sales
1	153745	156545
2	115253	118283
3	357241	275366
4	59237	377235
5	106995	171086
6	32721	71385
7	134992	262955
8	147764	244572
9	44117	270894
10	591034	1208072
11	160158	502013
12	283820	1302317
13	117429	154596
14	353731	742780
15	27118	159906
16	183778	674170
17	58178	79129
18	113117	165881
19	218614	322471
20	50730	162834
21	81443	215614
22	47041	76570
23	212040	1257489
24	33420	133121
25	83338	175502
26	60309	79330
27	114242	310071
28	47659	1025938
29	77724	109335
30	27374	62373
31	45303	61099
32	57042	48589
33	29309	67086
34	52201	62880
35	54606	73474
36	39040	61781
37	150692	508111
38	108781	294882
39	232105	238337
40	225568	506173
41	237946	408383
42	47676	76640
43	94521	437660
44	45270	152535
45	64878	291051
46	38201	73783
47	88563	166408
48	150910	129603