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STAT 213 Midterm: Statistics213Fall2015FormulaSheet

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jadeferret209
13 Mar 2016
School
University of Calgary
Department
Statistics
Course
STAT 213
Professor
Hua Shen

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STAT 213 Full Course Notes
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STAT 213 Full Course Notes
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Document Summary

Stat 213 formula sheet k = 1 + 3. 322(log(n)) s 2 = (x x )2 x 2 nx 2 n 1 n 1 k n. P(a b) = p(a) + p(b) p(a b) P(a c b c ) = p(a b)c. P(a ) = p(a b) + p(a b c ) P(a | b i )p(b i ) n pr n! (n r)! X = e( x ) = all x xp( x = x) 2 = var( x ) = e( x 2 ) e( x )2 x. E( x 2 ) = all x x 2 p( x = x) x. = sd( x ) = var( x ) P(x = x) = p x (1 p)1 x x = 0,1. X = e(x ) = p x. P x (1 p)n x x = 0,1, 2, 3,, n. X = e(x ) = np x. X e x! x = 0,1, 2, 3,

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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

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Related Questions

Q5. Let (Ω, F , P) be a probability space. Let λ > 0 be some constant.

  1. (a)  Give the definition of a random variable X on R ∪ {−∞, +∞}.

  2. (b)  Define the distribution function FX for the RV X.

[6 marks]

[1 marks]

[1 marks] (c) Suppose that Y is a RV on R ∪ {−∞, +∞} with distribution function given by

􏰄3 −1e−λy (y≥0)

[6 marks]

page1image62001664 page1image62003968

FY (y) = 4 2 1

(y < 0).
For any a < b, determine P(Y > a), and P(Y ∈ (a, b]). [3 marks]

  1. (d)  By noting {Y < b} = ∪n∈N{Y ≤ b − 1 } and using Continuity of Probability, n

    find P(Y < b). Similarly, find P(Y < ∞) and P(Y = −∞). [4 marks]

  2. (e)  Is Y either a discrete RV, or a continuous RV, or a mixture of both? Explain

    your answer. [1 marks]

9. Finally, you should write a program MontrealMaps which will suggest a path to go along the metro to get from one place to another. The only required method for MontrealMaps is a main method but of course you are allowed to write others. Your program should do the following. For any library methods that you use, make sure that you are properly importing things and handling any exceptions they may throw. (10 points) • Using an appropriate library method, you should create a Subway System object. If this method fails to initialize, you should print the message Error, not enough funding. • Use a Scanner and print statements to read the current x and y position of the user. • Use a Scanner and print statements to read the x and y position that the user wants to go to. . Find the nearest Metro Station to both the start position of the user and his final destination. • If the 2 metro stations have the same name (i.e. are the same metro station) then print It is fastest to walk there. • Otherwise, call the method findPath from the previous part to find a path from these 2 metro stations. . If the method returns null, then print Sorry, there is no path on the metro, you'll have to walk • Otherwise, print the path using the metro using the method printPath defined in the MapUtilities class in the appendix. SUMMARY OF JAVA STANDARD LIBRARY METHODS POR SELECTED CLASSES • String package java.lang) Methods - public boolean gist and e rs is stingeancoject - puble boolean grease Sering another ca t ering String paint i th Stre C h eshilly before the Stripe with striert w Single weiter water N ENE fusha -publish tohy Casting de . File( p age java.io) Methods r eate - publie Yiling path : C • Scanner (package java.ut 1) Method -ple S ule - double Double Sc - le bon when : S Scanner tal de fethede h able othebean - puble String Best Mus eethe u s tepal -pulle haalean haxtLine: Check the hea ther in left PrintStream( p age java.io) Methods pul vaid pri Pribonaat - puli wid pride d oble vile. - pille vaid print Print vei. -pulle vaid printject o: Prints Object -puli vaid printString : Prints String .. - vaid primi The theme line by writing the li n e tie id print in bool bl. Prise n value the - public void platinabled Prints double ved and then the line - public void printit Prints Ent value and then tomis the - Pull vaid pri l l be t he minime publie wild prin t ing with String in the terminates the line • ArrayLiat package java.util) Methods - public boolean Arraybettype was a new ArrayList

Hypothesis testing with ANOVA opinions about whether caffeine enhances test performance differ. You design a study to test the impact of drinks with different caffeine contents on students' test-taking abilities. You choose 21 students at random from your introductory psychology course to participate in your study. You randomly assign each student to one of three drinks, each with a different caffeine concentration, such that there are seven students assigned to each drink. You then give each of them a plain capsule containing the precise quantity of caffeine that would be consumed in their designated drink and have them take an arithmetic test 15 minutes later.

The students receive the following arithmetic test scores:

  Cola Black Tea Coffee  
Caffeine Content (mg/oz) 2.9 5.9 13.4  
  85 85 92 ∑X2 = 147,641
  86 89 87 G = 1,755
  82 82 80 N = 21
  75 75 89 k = 3
  66 88 96  
  78 76 83  
  87 82 92  
  T1 = 559 T2 = 559 T3 = 559  
  SS1 = 338.86 SS2 = 338.86 SS3 = 338.86  
  n1 = 7 n2 = 7 n3 = 7  
  M1 = 79.8571 M2 = 79.8571 M3 = 79.8571  

1.) You plan to use an ANOVA to test the impact of drinks with different caffeine contents on students' test-taking abilities. What is the null hypothesis?

(a) The population mean test score for the cola population is different from the population mean test score for the black tea population.

(b) The population mean test scores for all three treatments are equal.

(c) The population mean test scores for all three treatments are different.

(d) The population mean test scores for all three treatments are not all equal.

 

2.) Calculate the degrees of freedom and the variances for the following ANOVA table:

Source SS df MS
Between - - -
Within 702.28 - -
Total 973.14 -  

 

The formula for the F-ratio is:

 

 

3.) Using words, the formula of the F-ratio can be written as:

 

 

4.) Using the data from the ANOVA table given, the F-ratio can be written as:

 

5.) Calculate for F-ratio:

 

 

6.) At the level of significance, what is your conclusion?

(a)You can reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.

(b)You cannot reject the null hypothesis; caffeine does appear to affect test performance.

(c)You cannot reject the null hypothesis; you do not have enough evidence to say that caffeine affects test performance.

(d)You can reject the null hypothesis; caffeine does appear to affect test performance.