M & M Project. Think! Crunch those numbers! Answer!

Transcription

1 M & M Project Think! Crunch those numbers! Answer!

2 Chapters 1-2 Exploring Data and Describing Location in a Distribution

3 Univariate Data: Length Stemplot and Frequency Table Stem (Units Digit) Leaf (Tenths digit) Mean: 1.31 cm Variance:.019 cm Standard Deviation:.139 cm Range: 1.13 cm Length (cm) Frequency

4 Univariate Data: Length Histogram and Modified Boxplot 5-Number Summary:.6, 1.3, 1.3, 1.4, 1.9 IQR:.1

5 Univariate Data: Length Pie charts

6 Univariate Data: Length Density Curves

7 Chapter 3 Examining Relationships

8 Bivariate Data: Length and Width Scatter Plot Explanatory Variable X: Length (cm) Response Variable Y: Width (cm) LSRL Equation: ŷ= x r:

9 Bivariate Data: Length and Width Residual Plot r-squared:.0743

10 Chapter 4 More about Relationships between Two Variables

11 Nonlinear Data: Length and Mass Nonlinear Scatter Plot Explanatory Variable X: Length (cm) Response Variable Y: Mass (g) LSRL Equation: ŷ= x r: r-squared:.00016

12 Nonlinear Data: Length and Mass Transformed Scatter Plot Dimensional Transformation: Length Cubed LSRL Equation: ŷ= x 3 r: r-squared:.00081

13 Nonlinear Data: Length and Mass Residual Plot of Transformed Data Two Influential Outliers: 5.8 cm and 6.8 cm

14 Categorical Relationships Two-Way Table Color of M & M M On Blue Yellow Red Orange Green Brown Total Yes No Total Marginal Distributions: Yes: 79/107= 73.8% No: 28/107= 26.2% Blue: 21/107= 19.6% Yellow: 15/107= 14% Red: 8/107= 7.5% Orange: 19/107= 17.8% Green: 21/107= 19.6% Brown: 23/107= 21.5%

15 Chapter 5 Producing Data

16 Experimental Design Randomized Experiment Group 1: 50 Students Treatment 1: Taste Blue Treatment 1: Taste Blue 100 Students: Random Allocation Compare Results: Taste Preference Group 2: 50 Students Treatment 1: Taste Blue Treatment 1: Taste Blue

17 Chapter 6 Probability and Simulation

18 Probability Models Model One: Disjoint Event What is the probability than a flipped M & M will land M side up? S: { M side up, M side down} M up.56 M down.44

19 Probability Models Model Two: Non-Disjoint Event What is the probability than a randomly selected and flipped M & M will be orange and land M side up? S: {orange and M up, orange and M down, not orange and M up, not orange and M down} Orange.358 M up

20 Probability Models Two-Way Table M Side Blue Yellow Red Orange Green Brown Total Up Down Total

21 Chapter 7 Random Variables

22 Random Variables Discrete Random Variables Number of times a flipped M & M lands M side up

23 Random Variables Continuous Random Variables Distribution of mass

24 Chapter 8 Binomial and Geometric Models

25 Chapter 8 Binomial Questions Theoretical 107 M and M s are contained within a M and M packet. The probability that one will pick a red M and M at random is What is the probability of getting at least 3 red M and M s with replacement in 10 trials?

26 Binomial Distribution The mean of this data set is red M and M s. The standard deviation is reds away from the mean. The variance is

27 Chapter 8: Actual Binomial Trial # # of red M and M s picked In a sample size of 10 Probability of choosing a red M and M in trial

28 Geometric Questions 107 M and M s are contained within a M and M packet. The probability that one will pick a red M and M at random is What is the probability of picking the first red M and M at random on the 2th trial with replacement?

29 Actual Geometric Distribution Trial # Red M and M picked 2nd (1=yes, 0=no) The actual probability of picking the first red M and M at random on the 2th trial with replacement is 0.05.

30 Chapter 9 Sampling Distributions

31 Chapter 9 Distribution of Colors in the population

32 Chapter 9 Distribution of Colors in the population

33 The mean of the sampling distribution of p-hat is p= as. By the rule of thumb #1, the population size is greater than 10 times the sample size of 10 M and M s, so the standard deviation of p-hat is = Rule of thumb #2 does not apply in this situation because np>10 or n(1-p)>10, therefore a normal approximation may not be used. Due to the low frequency of red M and M s in our population, it would not be possible for rule of thumb # 2 to apply.

34 The End Thank you for watching our show!!!