Make and interpret the meaning of a 95% confidence interval for the production b

Question

Make and interpret the meaning of a 95% confidence interval for the production budget for all movies using the data given for the production budget for this sample of movies.

Source: boxofficemojo.com Winner of Best Picture Oscar Production Number of Year Picture Studio Box Office Noms Wins Release Budget run time % box office Theatres ($millions) ($million) (min) before nom 2015 Spotlight ORF 45.1 6 2 6-Nov 20 128 64 1227 2014 Birdman FoxS 42.3 9 4 17-Oct 18 119 62.8 1213 2013 12 Years a Slave FoxS 56.7 9 3 18-Oct 20 133 68.9 1474 2012 Argo WB 136.0 10 7 12-Oct 45 120 81.1 3247 2011 The Artist Wein 44.5 10 5 24-Nov 15 100 19.4 662 2010 The King's Speech Wein 135.5 12 4 25-Nov 15 118 57.9 1680 2009 The Hurt Locker Sum. 16.4 9 6 26-Jun 15 130 77.3 535 2008 Slumdog Millionaire FoxS 141.3 10 8 12-Nov 15 120 31.6 2943 2007 No Country for Old Men Mira. 74.3 8 4 9-Nov 14 122 65.8 2037 2006 The Departed WB 132.4 5 4 6-Oct 90 150 92 3017 2005 Crash Lions 54.6 6 3 6-May 6.5 100 97.8 1905 2004 Million Dollar Baby WB 100.5 7 4 15-Dec 30 137 8.5 2375 2003 The Lord of the Rings: The Return of the King NL 377.0 11 11 17-Dec 94 200 89.7 3703 2002 Chicago Mira. 170.7 13 6 27-Dec 45 107 37.8 2701 2001 A Beautiful Mind Uni. 170.7 8 4 21-Dec 58 136 66.6 2250 2000 Gladiator DW 187.7 12 5 5-May 103 155 99.4 3188 1999 American Beauty DW 130.1 8 5 15-Sep 15 122 57.4 1990 1998 Shakespeare in Love Mira. 100.3 13 7 11-Dec 25 123 36.4 2030 1997 Titanic Par. 600.8 14 11 19-Dec 200 194 56.4 3265 1996 The English Patient Mira. 78.7 12 9 15-Nov 27 162 53.8 1409 1995 Braveheart Par. 75.6 10 5 24-May 72 177 88.7 2037 1994 Forrest Gump Par. 329.7 13 6 6-Jul 55 141 91.2 2365 1993 Schindler's List Uni. 96.1 12 7 15-Dec 22 194 30.9 1389 1992 Unforgiven WB 101.2 9 4 7-Aug 18 131 74.4 2087 1991 The Silence of the Lambs Orion 130.7 7 5 14-Feb 19 118 100 1642 1990 Dances with Wolves Orion 184.2 12 7 9-Nov 22 183 56.6 1636 1989 Driving Miss Daisy WB 106.6 9 4 15-Dec 16 99 31.5 1668 1988 Rain Man MGM 172.8 8 4 16-Dec 25 133 56.1 1590 1987 The Last Emperor Col. 44.0 9 9 20-Nov 25 219 27.1 877 1986 Platoon Orion 138.5 8 4 19-Dec 6 120 28.4 1564 1985 Out of Africa Uni. 87.1 11 7 20-Dec 10 161 63.8 1102 1984 Amadeus Orion 51.6 11 8 21-Sep 8 158 49.9 802 1983 Terms of Endearment Par. 108.4 11 5 23-Nov 11 131 67.2 1259 1982 Gandhi Col. 52.8 11 8 10-Dec 22 188 22.5 825 1981 Chariots of Fire Col. 59.0 7 4 25-Sep 9 123 13.2 810 1980 Ordinary People Par. 54.8 7 4 19-Sep 7 124 100 1005 1979 Kramer Vs. Kramer Col. 106.3 10 5 19-Dec 8 105 45.7 898 1978 The Deer Hunter Uni. 49.0 9 5 8-Dec 7 183 87 902

Explanation / Answer

Rcode:

> df
data
1 20.0
2 18.0
3 20.0
4 45.0
5 15.0
6 15.0
7 15.0
8 15.0
9 14.0
10 90.0
11 6.5
12 30.0
13 94.0
14 45.0
15 58.0
16 103.0
17 15.0
18 25.0
19 200.0
20 27.0
21 72.0
22 55.0
23 22.0
24 18.0
25 19.0
26 22.0
27 16.0
28 25.0
29 25.0
30 6.0
31 10.0
32 8.0
33 11.0
34 22.0
35 9.0
36 7.0
37 8.0
38 7.0
> t.test(df$data)

   One Sample t-test

data: df$data
t = 5.3261, df = 37, p-value = 5.132e-06
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
20.09526 44.77316
sample estimates:
mean of x
32.43421

Answer:

The sample mean in this case is 32.43 $ million. 95% CI is 20.09526,44.77316. This means that 95 times out of 100 times the sample mean of the data will lie within this range.

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