AP Statistics Trimester II Project

Andrew Wang

Boris Leypunskiy Population of Interest Part I Sample 3 & 4 Sample 5 Sample 2 Part II Highest Worldwide Grossing US Films

511 Movies

Figures in millions of US dollars

*Data from BoxOfficeMojo.com Sample 1 (n = 20)

Simple Random Sample (SRS)

Excel: =INDEX($A:$A,RANDBETWEEN

(1,COUNTA($A:$A)),1) SRS (n = 25)

Mean: 378.8

Standard Dev: 181.9 SRS n = 35

Mean: 485.44

STDEV: 241.4 n = 50

Mean: 412.4

STDEV: 253.6 All Time Worldwide Grosses 1. Avatar (2009, Cameron) ... $2,782

2. Titanic (1997, Cameron) ... $2,185

3. The Avengers (2012, Wedon) ... $1,512 Notable Mentions Harry Potter and the Deathly Hallows Part I (2010, Yates) ... $956 (#18)

Gone with the Wind (1939, Fleming) ... $400 (#163)

The Godfather (1972, Coppola) ... $245 (#382) Our Population Sum: $204,664

N: 511

Mean: $400.52

Standard Dev: $249

Skewed Right 5 Number Summary Outliers? Min: 200.3

Q1: 244.4

Medium: 321.3

Q3: 457.7

Max: 2782.3 Inter Quartile Range: 213.3

Outlier if > 777.65 or < -75.95 42 Outliers 295.5

200.8

665.7

245.7

200.5

521.3

1004.6

934.4

381.1

363.9

550.5

321.7

401.1

361.8

221.3

709.8

341.6

223.7

307.1

291.6 Mean: 427.185

Standard Deviation: 235.14 296.2

229.7

441.3

694.7

796.7

563.7

348.8

413.1

591.7

359

221.3

413.1

282.8

209.1

239.6

415.7

225.9

227.8

783.8

1119.9

316.4

242.9

244.5

211.6 SRS n = 45

Mean: 387.8

STDEV: 231.3 Comparison n = 50

Mean: 412.4

STDEV: 253.6 N = 511

Mean: 400.52

STDEV: 249 Calculating Margin of Error 50 & 100 SRS of n =50 Analysis Calculating STDEV of Population

from STDEV of Means Confidence Intervals Conclusion Confidence Level: 95%, z*=1.96

m = Margin of Error, σ = standard deviation = 249.3, n = number of students in SRS= 50

m ≥ z*(σ/√n) = 1.96(249.3)/ √50 = 69.103 = 69.1

m ≥ 69.1 Data Analysis Tool Pack Sampling Tool

50 random samples, followed by an additional 50 samples to make 100 Histograms 50 SRS of size 50 100 SRS of size 50 Actual Mean: 400.52

Actual STDEV: 249 STDEV of Sample Means STDEV(Sample 50 means) = 31.65

STDEV(Sample 100 means) = 33.49 50 samples:

σx = σ/√n. σx = standard deviations of sample means ≈ 33.49, σ = standard deviation of the population = ?, n = sample size = 50.

31.65 * √50 = σ = 223.8 100 samples:

σx = σ/√n. σx = standard deviations of sample means ≈ 33.49, σ = standard deviation of the population = ?, n = sample size = 50.

33.49 * √50 = σ = 236.8 Actual STDEV: 249.5 Points outside the interval were calculated using the formula =COUNTIF(range, criteria)

Range = set of points on excel

Criteria = less than/ more than value x After taking several random samples we conclude that our confidence interval is correct.

In both samples, the mean was inside the interval approximately 95% of the time.

Further samples would bring our confidence interval even closer to our expected 95% confidence level.

Furthermore, both in our calculation of the means and the standard deviations, the more samples we used the closer we got to the actual result

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