Chapter 1 (Definitions)

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1 FINAL EXAM REVIEW Chapter 1 (Defiitios) Qualitative: Nomial: Ordial: Quatitative: Ordial: Iterval: Ratio: Observatioal Study: Desiged Experimet: Samplig: Cluster: Stratified: Systematic: Coveiece: Simple Radom:

2 Chapter 2 & 3 (Descriptive Statistics & Numerically Summarizig Data) 1. A city i the Pacific Northwest recorded its highest temperature at 96 degrees Fahreheit ad its lowest temperature at 28 degrees Fahreheit for a particular year. Use this iformatio to fid the upper ad lower limits of the first class if you wish to costruct a frequecy distributio with 10 classes. 2. Cosider the data set: {31, 35, 30, 32, 29, 52, 38, 27, 28, 30} a. Create a stem ad leaf plot. b. Determie IQR. c. What is the upper ad lower fece for outliers? d. Are there ay outliers? e. Create a box plot.

3 3. Determie the mea, media, mode, Q1, Q3, populatio stadard deviatio, sample stadard deviatio, populatio variatio, sample variatio of the followig data set: 15, 11, 5, 8, 12, 6, 13, 11, 11, 8 Chapter 4 (Relatioship of 2 Variables) 1. Fid the liear regressio lie give the followig data. x y

4 Chapter 5 & 6 (Probability & Discrete Probability Distributios) 1. What are the properties of a discrete probability distributio? 2. What is the missig probability if the oly outcomes are 0, 1, 2, or 3? x P(x) If a card is radomly selected from a complete set of a stadard deck of shuffle cards: A) P(red) = D) P(2) = B) P(face card)= E) P(15) = C) P(black jack)= 4. Use the data from the table of a radom sample of 121 college studets i Georgia to aswer the followig: Nosmoker Smoker TOTAL Male Female TOTAL A) Fid the probability of radomly selectig ay perso from the sample ad the perso beig either a male-smoker or a femaleosmoker. B) Fid the probability of radomly selectig a perso from the group that is a smoker give that the perso is a male? C) P(female smoker)

5 Chapter 7 (Normal Probability Distributios) 1. Fid the area uder the stadard ormal curve betwee z = -1.2 ad z = Fid P(z > 1.8) 3. The average overall score o the SAT last year was a 1500 with a stadard deviatio of 300. The average overall score o the ACT last year was 21 with a stadard deviatio of 5. a. What is the z-score associated with a studet scorig a 1750 o the SAT? b. What is the z-score associated with a studet scorig a 25 o the ACT? c. Which score is better? Chapter 8 (Samplig Distributios) 1. (Cetral Limit Theorem) The mea height of a male i the Uited States is roughly 69 iches (5 feet 9 iches) with a stadard deviatio of approximately 3 iches. a. Give samples of size 16 were radomly take, what would be the mea of the sample meas ( ) ad the stadard deviatio of the sample meas ( )? b. A radom sample of 16 males from the Uited States was take. What is the probability that the average height of the group was greater tha 6 feet (72 iches)?

6 Chapter 9 (Cofidece Itervals) 1. The populatio stadard deviatio of the SAT is kow to be 300 ad the populatio is approximately ormal. If a radom sample of 16 studets had a mea score of 1560, costruct a 99% cofidece iterval for the populatio mea. 2. A radom sample of 16 females from the Uited States was take. The mea height of the females from the sample was 64 iches ad the sample stadard deviatio was 4 iches. Costruct a 95% cofidece iterval for the populatio mea. 3. Give a sample {13, 15, 19, 10, 13, 12, 10, 18, 12, 12} costruct a 90% cofidece iterval for the populatio mea.

7 Chapter 10 (Hypothesis Testig) 1. A evirometal agecy wats to see if the ew govermet policies have helped the auto idustry to icrease fuel efficiecy of compact car models. Five years ago the average fuel efficiecy was 22 mpg. a. State the ull hypothesis. b. State the alterate hypothesis. c. What would a Type I error suggest? d. What would a Type II error suggest? 2. If we wish to support the claim 20 at a level of sigi icace of = Give the sample statistics = 30, =19.2 ad =4, a. What is the ull hypothesis (H0)? b. Compute the value of the test statistic. c. What are the critical t-values? d. What does the test statistic suggest?

8 3. A cosumer group believes that a particular compay that makes sacks is t givig less tha the amout of chips that is labeled o the bag. The bag suggests the weight of chips to be 24 grams. The group takes a radom sample of 30 bags ad fids the sample mea to be 27 grams with a stadard deviatio of 0.8 grams. a. State H0 ad H1 b. Compute the test statistic. c. Determie the critical t-value. d. Should we reject or fail to reject H0? 4. If we wish to support the claim 20 at a level of sigificace of = Give the sample statistics = 16, =22, =4, ad that the populatio is approximately ormal, determie the P-value. 5. If we wish to support the claim 20 at a level of sigificace of = Give the sample statistics = 25, =18, s = 2, ad it has bee cocluded that the sample appears to come from a populatio that is ormally distributed based o a ormality probability plot. a. Fid the stadardized test statistic t. b. Fid the P-Value usig a t-distributio.

9 Chapter 11 ad 12 (Iferece about 2 meas & Chi Squared) 1. Usig a iferece about two meas of idepedet samples. Attempt to validate the claim 1 2 at a level of sigificace of = The provided statistics: 1 = 16, 1=18, s1 = 2 ad 2 = 16, 2=22, s2 = 3 a. Fid the stadardized test statistic t. b. Fid the P-Value usig a t-distributio. 2. Usig = 0.10 ad a Chi-Square test of goodess of fit determie the followig. Cards are draw oe at a time with replacemet from a stadard deck of shuffled cards ad the frequecy that each suit appears is recorded. Each suit should appear approximately ¼ of the time whe selected. A player suspects that the deck is ot stadard because too may clubs are appearig. The results of the 100 radom draws are show below. Suit Hearts Clubs Diamods Spades Frequecy A) State H0. B) State H1. C) Fid the chi-square test statistic. D) Fid the p-value. E) What is the coclusio?

10 Descriptive Statistics Sample mea: x = x i Sample stadard deviatio: s = (x i x ) 2 Probability 1 Rule of additio: P(A B) = P(A) + P(B) P(A B) Rule of multiplicatio: P(A B) = P(A)P(B A) Iferetial Statistics Mea of the distributio of the sample mea: μ x = μ Stadard deviatio of the distributio of the sample mea: σ x = σ Mea of the distributio of the sample proportio: μ p = p Stadard deviatio of the distributio of the sample proportio: σ p = p(1 p) Commo critical values: z 0.10 = z 0.05 = z = z 0.01 = z = Cofidece iterval: Sample statistic ± critical value * stadard error of the statistic o x ± z /2 σ = ( z /2 σ ) 2 e o x ± t /2,df s o (x 1 ) x 2 ± t /2,df s s Stadardized test statistic: (statistic parameter)/(stadard deviatio of the statistic) o z = x μ 0 σ o t = x μ 0 s o t = (x x 1 ) (μ 2 1 μ 2 ) s s 2 2 2

11 Chapter 7: Formula Sheet for Math 1431 Chapter 9: Z = X μ σ ; X = μ + Zσ (1 ) 100% CI for μ: x ± z σ ; 30 2 Chapter 8: μ x = μ ; p = x σ x = σ (1 ) 100% CI for μ: (1 ) 100% CI for p: x ± t 2 p ± z 2 p (1 p ) 10 ad 0.05N s ; df = 1 p (1 p ) ; μ p = p; p(1 p) σ p = = ( z σ 2 E )2 z = x μ σ or z = p p p(1 p) Commo Critical Values: z 0.10 = z 0.05 = z = z 0.01 = z = Chapter 10: z 0 = x μ 0 σ z 0 = p p 0 p 0 (1 p 0) = p (1 p )( z /2 E )2 = 0. 25( z /2 E )2 if p 0 (1 p 0 ) 10 ad 0.05N Chapter 11: t o = x μ 0, with df=-1 s t 0 = d μ d s d CI for matched-pairs data: d ± t /2,df s d t 0 = (x 1 x ) 2 (μ 1 μ 2 ) s s CI for μ 1 μ 2 : (x 1 ) x 2 ± t /2,df s s z 0 = (p 1 p 2 ) (p 1 p 2 ) CI for p 1 p 2 : p (1 p )( ), where p = x 1 + x (p 1 p 2 ) ± z /2 p 1(1 p 1 ) 1 + p 2(1 p 2 ) 2 = 1 = 2 = [p 1 (1 p 1 ) + p 2 (1 p 2 )]( z /2 E )2 = 1 = 2 = 0. 5( z /2 E )2 Chapter 12: E i = μ i = p i for i = 1, 2,, k χ 2 = (O i E i ) 2 E i for i = 1, 2,, k

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