Calculate The Descriptive Statistics From

Required: A. Calculate the descriptive statistics from the data and display in a table. Be sure tocomment on the central tendency, variability and shape for each variable. B. Draw a graph that displays the distribution of admissions. C. Create a box-and-whisker plot for the distribution of the variable Top Price anddescribe the shape of the distribution. Is there evidence of outliers in the data?D. What is the likelihood that the admissions are greater than 70 million if the real priceof tickets exceeds $20. 00? Are admissions statistically independent of price? Use aContingency Table. E. Estimate the 95% confidence interval for the population mean theatre capacity andcomment on it. F. Your supervisor recently stated that theatre admissions from 2008 through 2014 (ie. last 7 years) have exceeded the admissions in Taiwan which have been a constant 84million per year. Test her claim at the 5% level of significance. G. Run a multiple linear regression using the data and show the output from Excel. H. Is the coefficient estimate for the real ticket price in 2014 $ different than zero at the5% level of significance? Set-up the correct hypothesis test using the results found inthe table in Part (G) using both the critical value and p-value approach. Interpret thecoefficient estimate of the slope. I. Interpret the remaining slope coefficient estimates. Comment on whether the signs arewhat you are expecting. J. Interpret the value of the Adjusted R2. Is the overall model statistically significant at the5% level of significance? Use the p-value approach. K. Do the results suggest that the data satisfy the assumptions of a linear regression: Linearity, Normality of the Errors, and Homoscedasticity of Errors? Show using scatterdiagrams, normal probability plots and/or histograms and Explain. L. Based on the results of the regressions, is it likely that other factors have influencedthe theatre admissions? If so, provide a couple possible examples and indicatewhether these would likely influence the regression results if they were included. M. If a community housing organisation asked for information regarding thecharacteristics of housing targeting the households of native born Australians, explainwhether a simple random sampling technique would provide an accuraterepresentation of these households. (Note: This question does not use the data)19. 2519. 2519. 2519. 43519. 43519. 43519. 6619. 6619. 6620. 0420. 0420. 0420. 7620. 7620. 7619. 2520. 7619. 43520. 0419. 43520. 040. 511. 50. 511. 50. 511. 50. 511. 50. 511. 5110. 50. 51. 51. 5Year199419951996199719981999200020012002200320042005200620072008200920102011201220132014Admissions (millions) Y Screens Theatres Films Screened Real Ticket Price Capacity (‘000s)28. 982270222319. 7137729. 774257319419. 8232435. 567650923919. 929530. 864550625919. 6330337. 471252028119. 662853977250129119. 432864385151025220. 4129546. 988552224019. 2530147. 290651022919. 3929655. 595151825919. 4430068. 1102853725220. 7631269. 9113755725320. 5433273. 9125155128120. 2135676142256328520. 0838780157656727319. 8441388174858025519. 5444682. 2181755425019. 3845392. 5185554724519. 346392. 5187254725819. 5246489. 8190755326819. 5647191. 5190952031820460AdmissionsMeanStandard ErrorMedianModeStandard DeviationSample VarianceKurtosisSkewnessRangeMinimumMaximumSumCountScreens61. 823809524 1213. 5245. 1518046064 103. 660968. 1102892. 5#N/A23. 608534575 475. 034557. 36290476 225657. 3-1. 6663464306 -1. 569617-0. 0555289741 0. 41001463. 6126428. 964592. 519091298. 3254842121Theatres Films screened Real ticket price545. 09529. 45840654752043. 343861878. 698. 3758222. 4453132015017021144721257. 380952381 19. 77952380955. 76957380220. 091997609225519. 66259#N/A26. 43950867640. 4215860077699. 0476190480. 17773476191. 25632628570. 0850433316-0. 05708383710. 91600328011241. 5119419. 2531820. 765405415. 372121Capacity (‘000s)362. 809523809515. 570824220133229571. 35448062155091. 461904762-1. 58299691890. 4435730696186285471761921Frequencies (Admissions (millions))BINS Frequency Percentage Cumulative %2500. 00%0. 00%35314. 29%14. 29%45419. 05%33. 33%5529. 52%42. 86%6514. 76%47. 62%75314. 29%61. 90%85314. 29%76. 19%95523. 81%100. 00%The distribution is left skewedMedian68. 1Mean61. 82Histogram654Frequency32102535455565BINS7535Histogram120. 00%100. 00%80. 00%60. 00%40. 00%20. 00%455565BINS7585950. 00%FrequencyCumulative %Five-number SummaryMinimum19. 25First Quartile19. 435Median19. 66Third Quartile20. 04Maximum20. 76Box-and-whisker Plo2101919. 219. 419. 619. 8Box-and-whisker Plot – Real Ticket Price19. 619. 82020. 220. 420. 620. 821Q) What is the likelihood that the admissions are greater than 70 million if the real price of tickets exceeds $20. 00? Are admA) There is a 40% probability. Admissions are statistically independent of priceContingency tablesYear199419951996199719981999200020012002200320042005200620072008200920102011201220132014Admissions (millions) Real Ticket Price28. 919. 7129. 719. 8235. 519. 930. 819. 6337. 419. 663919. 434320. 4146. 919. 2547. 219. 3955. 519. 4468. 120. 7669. 920. 5473. 920. 217620. 088019. 848819. 5482. 219. 3892. 519. 392. 519. 5289. 819. 5691. 520P(B) – Price exceeds $20P(B’) – Price equal to or less than $20Joint and marginal probabilityP(B) – Price exceeds $20P(B’) – Price equal to or less than $20Conditional probabilityP(B) – Price exceeds $20P(B’) – Price equal to or less than $2012xceeds $20. 00? Are admissions statistically independent of price? Use a Contingency Table. P(A) – Admissions greater than 70mP(A’)Admissions equal to or less than 70m279P(A) – Admissions greater than 70m3912P(A’)Admissions equal to or less than 70m0. 09523809520. 33333333330. 4285714286P(A) – Admissions greater than 70m516210. 1428571429 0. 2380950. 4285714286 0. 7619050. 57142857141P(A’)Admissions equal to or less than 70m0. 40. 43750. 60. 5625Conditional probabilityP(A|B) = P(A and B)/P(B)IndependenceP(A, given that B occurs) = P(A)P(B, given that A occurs) = P(B)P(A and B) = P(A)*P(B)xxx*EXPLAIN FURTHERJointMarginalConfidence Interval Estimate for the MeanDataSample Standard DeviationSample MeanSample SizeConfidence Level69. 551552255357. 952095%Intermediate CalculationsStandard Error of the Mean15. 552199878Degrees of Freedom19t Value2. 0930240544Interval Half Width32. 551128444Confidence IntervalInterval Lower LimitInterval Upper Limit*Comment on above*!!!325. 40390. 50Admissions (‘000s)Original Taiwan200880200988201082. 2201192. 5201292. 5201389. 8201491. 584848484848484DOUBLE CHECK ALL OF THISDescriptive statisticsOriginalMeanStandard ErrorMedianModeStandard DeviationSample VarianceKurtosisSkewnessRangeMinimumMaximumSumCount88. 0711. 91289. 892. 55. 0625. 60-0. 88-0. 9212. 58092. 5616. 57t Test for Hypothesis of the MeanNull HypothesisDatam &gt,Level of SignificanceSample SizeSample MeanSample Standard Deviation840. 05788. 075. 06Intermediate CalculationsStandard Error of the Mean1. 9125002334Degrees of Freedom6t Test Statistic2. 1281043154Lower-Tail TestLower Critical Value-1. 9431802805p-Value0. 9612940976Do not reject the null hypothesisCalculations AreaFor one-tailed tests: TDIST valu 0. 0387061-TDIST va 0. 961294Regression AnalysisRegression StatisticsMultiple RR SquareAdjusted R SquareStandard ErrorObservations0. 98925023780. 9786160330. 9714880443. 986415259621ANOVAdfRegressionResidualTotalSSMSF5 10908. 8854959 2181. 7770992 137. 2920234115 238. 372599327 15. 89150662220 11147. 2580952Coefficients-71. 88116558060. 08783691740. 0450879570. 00178636935. 2766367818-0. 2819484599InterceptScreensTheatresFilms ScreenedReal Ticket PriceCapacity (‘000s)Standard Errort StatP-value47. 5443639849 -1. 5118756369 0. 15134537690. 0094386683 9. 3060710545 1. 27616E-0070. 0347085942 1. 2990430181 0. 21354317320. 0415134777 0. 0430310685 0. 96624436022. 4119007809 2. 1877503518 0. 04493298610. 0673168093 -4. 1883812211 0. 0007912603RESIDUAL OUTPUTObservation123456789101112131415161718Predicted Admissions (millions) Y30. 078828278732. 707422145632. 703579247626. 200818712137. 989795084240. 925627719950. 83443531346. 527920131149. 960261299753. 463255318264. 652643590168. 330583807569. 615429815875. 757378616480. 846126509785. 620774887287. 682402356387. 4540421309Residuals-1. 1788282787-3. 00742214562. 79642075244. 5991812879-0. 5897950842-1. 9256277199-7. 8344353130. 3720798689-2. 76026129972. 03674468183. 44735640991. 56941619254. 28457018420. 2426213836-0. 84612650972. 3792251128-5. 48240235635. 045957869119202189. 8494041601 2. 650595839991. 4495139566 -1. 649513956695. 6497569193 -4. 1497569193Significance F5. 651799E-012Lower 95%Upper 95%-173. 21957859 29. 4572474290. 0677188723 0. 1079549626-0. 0288916604 0. 1190675744-0. 0866975139 0. 09027025260. 1357919585 10. 417481605-0. 4254308425 -0. 1384660773*p-value is less than 0. 05 so that means we need to reject the null hypothesis?eject the null hypothesis?

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