Bar Chart of Producers. A. Grimaldi MGM. Colum./Univers. USSR/Japan. Horizon Pict. Columbia Pict. Universal Pict. Enigma Prod. 20th Cent.
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1 Statistics on Movie DVD s by David Gurney The data for this project came from the Movies Unlimited website and the Critics Choice website on July 3, 211. The variables were the movie producer, the length of the move in minutes, the cost at Movies Unlimited and the cost at Critics Choice. When multiple producers were listed, the most well-known was chosen. I decided Columbia and Universal were equally well-known, and so listed them both for their joint production of the Electric Horseman. When multiple prices were listed, the lowest price was chosen. There were three different versions of Close Encounters of the Third Kind in theaters at one time or another, so the length of the original theatrical release was chosen. A frequency distribution for the producers is shown below and a bar chart follows. Producer Frequency Relative Frequency 2 th Century Fox Alberto Grimaldi 1.25 Amblin Entertainment 1.25 Columbia Pictures 1.25 Columbia/Universal Enigma Production 1.25 Horizon Pictures 1.25 Imagine Entertainment 1.25 Metro-Goldwyn-Mayer 6.15 Miramax Films 1.25 Orion Pictures 1.25 Paramount Pictures 1.25 Tig Productions 1.25 Touchstone Pictures 2.5 TriStar Pictures 2.5 Universal Pictures 1.25 USSR/Japan 1.25 Warner Brothers Bar Chart of Producers 2th Cent. Fox A. Grimaldi Amblin Enter. Columbia Pict. Colum./Univers. Enigma Prod. Horizon Pict. Imagine Enter. MGM Miramax Films Orion Pictures Paramount Pict. Tig Productions Touchstone Pict. TriStar Pictures Universal Pict. USSR/Japan Warner Bros.
2 2 th Century Fox has the highest frequency at 7. Metro-Goldwyn-Mayer and Warner Brothers are tied for second with a frequency of 6. Columbia Pictures is alone in third with a frequency of 5. Touchstone Pictures and TriStar Pictures are tied for fourth and somewhat below the first three places with a frequency of 2. All the other producers occur just once. A chi-square goodness of fit test was used to see if the producers were equally likely to occur. The resulting test statistic was 34.7 and the corresponding P-value was.68. So at 95% confidence, the evidence is strong enough to say that not all the producers are equally likely. The basic statistics for this data are shown in the table below. Lengths Movies Unlimited Prices Critic s Choice Prices mean mode 15 (3 times) 12.74, (6 times) (15 times) minimum first quartile median third quartile maximum range standard deviation interquartile range The following is a histogram of the movie lengths. The maximum is 2 and the minimum is 81. The histogram is skewed right with a peak at 118. There are no gaps and no extreme values. Frequency Histogram of Movie Lengths Length in Minutes
3 The histogram of the Movies Unlimited prices is shown below. The minimum is $8.99 and the maximum is $ The histogram is skewed right with a single peak at $ There is a gap at $26.48, but there are no extreme values. 25 Histogram of Movies Unlimited Prices 2 Frequency $11.48 $16.48 $21.48 $26.48 $31.48 Price The histogram of the Critic s Choice prices is shown below. The minimum is $5.92 and the maximum is $ The histogram is skewed to the right with one peak at $ There is a gap at $19.92, but there are no extreme values. 25 Histogram of Critic's Choice Prices 2 Frequency $7.92 $11.92 $15.92 $19.92 $23.92 Price
4 The following is a modified boxplot for the lengths of the movies in minutes. The boxplot is skewed right with two outliers on the high side at 191 and 2 minutes. Modified Boxplot of Movie Lengths The median, third quartile and new maximum for Critic s Choice are so close together that they are indistinguishable. Critic s Choice has eight outliers on the low end and 9 outliers on the high end. Movies Unlimited only has one outlier on the high end. With the outliers, Movies Unlimited has the highest price and Critic s Choice has the lowest price. But if the outliers are ignored, then Movies Unlimited still has the highest but also lowest price; in addition, Movies Unlimited has the largest range and interquartile range, and its median is larger than the Critic s Choice median. A paired-t test was used to determine if the means of the prices for Movies Unlimited and Critic s Choice DVD s are different. The test statistic was 2.73 and the resulting P-value was.9. So at 95% confidence, the evidence is strong enough to say that the means of the prices for Movies Unlimited and Critic s Choice are different. The 95% confidence intervals for the means of the quantitative variables are shown below. Movie Length (12.5, 138.6) Movies Unlimited Prices (12.8, 15.38) Critic s Choice Prices (11.72, 14.27) The three quantitative variables were tested to see if they were normally distributed using the Ryan- Joiner test. The tests were run at 95% confidence and since there are 4 films, the critical value for each of these tests is.972 according to Looney & Gulledge, The American Statistician, vol. 39, no. 1 (1985), pages 74 to 79. The test statistics for each of the variables are shown in the table below. Since each of the test statistics is less than the critical value, we can say with 95% confidence that each of the quantitative variables is not normally distributed.
5 Variable Test Statistic Movie Length.965 Movies Unlimited Price.93 Critic s Choice Price.919 The scatter diagram of the Movies Unlimited price versus the movie length is shown below. $3 Movies Unlimited Price Versus Movie Length $25 Movies Unlimited Price $2 $15 $1 $ Movie Length The equation of the regression line is: y =.311x The regression line is the solid black line on the scatter diagram. The point at 11 minutes and $29.99 is the outlier. The point at 81 minutes and $16.99 is an influential observation. The coefficient of determination is.48, which means that about 4.8% of the variation in the scatter diagram is determined by the regression line, 95.2% of the variation is determined by other factors. The correlation coefficient is.219. A test for significant linear correlation was run and the resulting P- value was.174. Thus at 95% confidence, there is no significant linear correlation. This conclusion is supported by the scatter diagram.
6 Project Data Movie Name Producer Length Movies Critic s (minutes) Unlimited Choice The Abyss 2 th Century Fox 171 $14.99 $12.71 The African Queen Horizon Pictures 15 $16.99 $23.96 The Alamo Metro-Goldwyn-Mayer 162 $12.74 $12.73 Apollo 13 Imagine Entertainment 14 $12.74 $12.73 Awakenings Columbia Pictures 12 $ 9.99 $ 8.48 Bad Day at Black Rock Warner Brothers 81 $16.99 $16.96 Batteries Not Included Amblin Entertainment 17 $ 9.99 $ 5.93 Breaking Away 2 th Century Fox 1 $ 8.99 $ 8.49 Broken Arrow (1996) 2 th Century Fox 11 $ 9.99 $ 8.48 Cannery Row Metro-Goldwyn-Mayer 12 $16.99 $16.96 Chariots of Fire Enigma Productions 124 $12.74 $12.72 Cliffhanger TriStar Pictures 118 $ 9.99 $ 8.48 Close Encounters of the Columbia Pictures 135 $15.99 $16.96 Third Kind Con Air Touchstone 115 $21.59 $12.71 Cool Hand Luke Warner Brothers 126 $16.99 $16.96 Dances With Wolves Tig Productions 181 $16.99 $16.96 Derzu Uzalla USSR/Japan 11 $29.99 $25.46 Dirty Harry Warner Brothers 12 $11.99 $12.71 Doctor Zhivago Metro-Goldwyn-Mayer 2 $2.99 $12.71 Driving Miss Daisy Warner Brothers 99 $12.74 $12.71 Eddie and the Cruisers Metro-Goldwyn-Mayer 95 $12.74 $12.7 The Electric Horseman Columbia/Universal 121 $12.74 $12.71 The English Patient Miramax Films 162 $17.99 $16.96 Executive Decision Warner Brothers 133 $ 8.99 $ 5.92 Face Off Paramount Pictures 138 $14.99 $11.1 Father of the Bride (1991) Touchstone Pictures 15 $13.49 $12.74 First Knight Columbia Pictures 134 $14.99 $12.7 A Fish Called Wanda Metro-Goldwyn-Mayer 18 $14.99 $12.71 Fly Away Home Columbia Pictures 18 $11.99 $12.71 French Kiss 2 th Century Fox 111 $ 8.99 $ 8.48 The Fugitive (1993) Warner Brothers 13 $11.99 $11.1 Ghandi Columbia Pictures 191 $15.99 $16.96 The Good, the Bad & Alberto Grimaldi 179 $13.49 $12.71 the Ugly Gorky Park Orion Pictures 127 $14.99 $12.71 The Grapes of Wrath 2 th Century Fox 129 $12.99 $12.71 The Great Escape Metro-Goldwyn-Mayer 172 $13.49 $12.71 Independence Day 2 th Century Fox 145 $14.99 $12.71 The Jackal Universal Pictures 125 $12.74 $12.71 Jerry Maguire TriStar Pictures 139 $11.99 $12.71 Jumping Jack Flash 2 th Century Fox 15 $ 8.99 $ 8.48
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