Review - Exam 1 - Spring2024

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New York University *

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Statistics

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Apr 3, 2024

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– Exam 1 REVIEW QUESTIONS - 1. Below is a scatterplot of the Drop (in feet) of a rollercoaster’s largest drop and the maximum speed of the rollercoaster. a) Circle the direction of the relationship between Drop and Speed POSITIVE NEGATIVE b) What are the 3 conditions of correlation and does it pass that condition 1) quantitative variables Does it meet this condition? YES NO 2) straight enough Does it meet this condition? YES NO 3) no outliers  no extreme outliers are shown in the graph Does it meet this condition? YES NO c) If a rollercoaster with a Drop of 250 feet and a Speed of 50 mph was added to the plot, what would happen to r? (Circle the best answer) estimate: r=0.86  r=0.79 r would stay the same r would increase r would decrease OTHER question examples: d) CASE 1: r=-0.98 p—value= 0.17 vs CASE 2 : r=0.45 p-value= 0.0007 1

– Exam 1 REVIEW QUESTIONS - e) CASE 3: R 2. Consider the following JMP output from whether Students from two Stats 201 Sections did better on Exam 2 than Exam 1. a) What percent of Section B did better on Exam 2? 30 49 = 0.61224  61.1% b) What percent of the Section A did better on Exam 1? 21 87 = 0.24137  24.3% c) What percent of the Students did better on Exam 2? 96 136 = 0.70588  70.6% d) What visual graphic (or tool) could you use to see differences between the Sections? - Mosaic plot, segmented bar chart, side-by-side pie charts  contingency table 2

– Exam 1 REVIEW QUESTIONS - 3. Given below are the boxplots of annual emissions in kilotons of methane gas from a group of countries. a) Which country has the highest median emission of methane? - Italy b) Which one describes the shape of the distribution of methane emissions in Romania? i. Skewed right ii. Symmetric iii. Skewed left c) Which of the following statements is FALSE? i. Italy’s minimum emission is more than Turkey’s minimum. TRUE ii. Japan’s median emission is less than Turkey’s median emission TRUE iii. Romania had the year with the highest emission. TRUE iv. New Zealand was the least consistent on emission levels. d) Approximately what value is the 75th Percentile for emission in Japan? - About 43,000 e) Approximately what value is Q1 for emission for Romania? - About 34,000 3

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– Exam 1 REVIEW QUESTIONS - 4

– Exam 1 REVIEW QUESTIONS - 4. The speed limit is 25 mph on Cumberland Avenue. During the construction along Cumberland Avenue, assume that the speed of cars follows the normal model with mean 22.53 mph and a standard deviation of 2.47 mph. a) Find the z-score for the speed limit. Z = (value – mean)/SD  (25-22.53)/2.47= 1 b) What percent of cars would you expect to be going over the speed limit? Using the 68-95-99.7 rule  16% Using the tool  15.87% c) If a car is captured on radar at 28 mph, would you consider the speed of the car unusual? Justify your answer. Z= (28-22.53)/2.47 = 2.2146  less than 3  not an outlier d) What percent of cars would be driving with 28 mph or slower? Using only the 68-95-99.7 rule, provide as narrow of an interval as you can that contains the answer to this question. Fill in the blanks below. The answer is greater than 97.5% but less than 99.85 % 5

– Exam 1 REVIEW QUESTIONS - Graph 1 N(98.2, 0.7) Area below 99.1 F is 0.9007 Graph 2 N(98.2, 0.7) Area outside of 97.14 and 99.26 is 0.13 Graph 3 N(0, 1) The bottom 94% is below 1.555 Graph 4 N(0,1) The middle 60% is between -0.842 and 0.842 6

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– Exam 1 REVIEW QUESTIONS - 5. In a 1992 article in the Journal of the American Medical Association, researchers reported that a more accurate figure may be an average of 98.2°F. Furthermore, the standard deviation appeared to be around 0.7°F. Assume that a Normal model is appropriate N(98.2, 0.7). Use the graphics on the previous page to answer the following questions. a) What percent of the people had body temperatures lower than 97.14 ° F? Area = 0.13/2 = 0.065  6.5% b) What percent of the people had body temperatures higher than a z-score of 1.286? 99.1-99.2/0.7 = 1.286 (z-score of Graph 1) Z= 1.286 matched up with the value =99.1 F so 1 st picture is what we need percentage = 1 - 0.9007 as we want “above” area rather than the given “below” area percentage = 0.0993  9.93% c) What percent of people have body temperatures between 98.2 °F and 99.26 °F ? 100 – 13 = 87%  87/2 = 43.5% As we know the two tails below and above add up to 13%, the “between” area is 87% and we need the upper half, which is 87.2 = 43.5% d) What body temperature is at the 20 th Percentile? z-score we want is -0.842 z= (value – mean)/ SD = -0.842 = (value – 98.2)/0.7 -0.842(0.7) = (value -98.2) -0.842(0.7)+98.2 = value  97.61 7

– Exam 1 REVIEW QUESTIONS - 6. Consider the following list of numbers: 23, 2, 15, 4, 9, 18, 6, 22, 5,27 a) Report the mean: Add them up then divide by total number: (23 + 2 + 15 + 4 + 9 +18 +6 + 22 + 5 + 27)/10 = 13.1 b) Report the median: Put number in order from least to greatest 2, 4, 5, 6, 9, 15, 18, 22, 25, 27 Median = (9+15)/2 = 12 c) Report Q1: 2, 4, 5, 6, 9 Q1  5 d) Report Q3: 15, 18, 22, 25, 27 Q3  22 e) Report the IQR: IQR  22- 5 = 17 8

– Exam 1 REVIEW QUESTIONS - 7. Circle the appropriate data type for each graphical display. UNIVARIATE a) Pie Chart b) Histogram Quantitative Categorical Quantitative Categorical c) Stem and Leaf d) Bar chart Quantitative Categorical Quantitative Categorical e) Dot Plot e) Pareto chart Quantitative Categorical Quantitative Categorical BIVARIATE Match the correct variable combination with the data visualization type (you may use a combination more than once). Visualization Variable Combination Segmented Bar Chart ___ A __ A) 2 Categorical Variables Side By Side Box Plot __ B ___ B) 1 Categorical, 1 Quantitative Stacked Histogram _____ C) 2 Quantitative Variables Mosaic Plot __ A ___ Scatterplot __ C ___ Contingency Table ___ A __ 9

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– Exam 1 REVIEW QUESTIONS - TRUE/FALSE T F Simulations mimic reality by using random numbers to represent outcomes of real events. T F A sample statistic is analyzed to make inferences about a population parameter. T F When the correlation is above 0.90 or below -0.90, it is safe to conclude that changes in X cause changes in Y. T F Outliers can drastically impact the value of r. T F Correlation is described with shape, center and spread. T F When checking the significance of a correlation coefficient, a p-value of 0.01 would imply that the correlation is not significant (i.e. possibly due to random chance). T F If one knows the mean and standard deviation of a data set, then all values in the data set can be converted into z-scores. Values—y’s  z = (y-mean)/SD  zscores T F The straighter the line in a Normal Probability plot, the more likely the data will pass the Nearly Normal Condition. Fill in the Table with the correct symbol: Name Symbol Observed Data Value y Sample Average Sample Standard Deviation s Distribution Mean Typeequationhere. Distribution Standard Deviation Normal Distribution (with mean of μ and standard deviation of σ) N ( μ,σ ) Correlation Coefficient r 10

Review - Exam 1 - Spring2024

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