Chapter 1 Introduction to Statistics

Chapter 2 Summarizing and Graphing

Chapter 3 Statistics for Describing, Exploring, and Comparing

DataMidpoint(x)Frequency (f)x^2f*xf*x^2Finding the Mean and Standard Deviation from a Frequency DistributionL1: Enter x values (midpoints 4 freq. dist.)L2: frequencies or probabilities as applicable.1-Var Stats (L1, L2) ENTERMean (x-bar) and Standard Deviation: Sx (Freq.) or x (Probability)

Chapter 4 Probability

Combination: nCr (n objects taken r at a time; order doesnt matter)Combinations Rule1. n different items available.2. Select r items without replacement3. Same items rearranged are considered the same sequence Permutation: nPr (n objects taken r at a time; order does matter)Permutations Rule (Items all Different)1. n different items available.2. Select r items without replacement3. Same items rearranged are considered different sequences Factorial: ! (n objects arranged in order n! different ways)

Chapter 5 Discrete Probability Distributions

Binomial Rules:

1. 2 outcomes 2. Fixed # of trials 3. Probabilities are constant 4. Events are independent

p = probability of success q = probability of failure n = number of trials

To find P(x = #) binompdf (n, p, x) = P(X = x exactly)Or... To find P(x < #) binomcdf (n, p, x) = P(X x... AT most x) Eg. P(0)+P(1)+P(2)+... +P(x) Or 1-P(at most 17)At most/less than or equal to: binomcdf(n,p,x)Less than:< binomcdf(n,p,x-1)At least/greater than or equal to: 1 minus binomcdf(n,p,x-1)Greater than/more than:> 1 minus binomcdf(n,p,x)

Chapter 6 Normal Probability Distributions

To find a probability if a Z-score is known: normalcdf: (LOW, HIGH)You are given a point (value) and asked to find the corresponding area (probability) If given x-scores, mean & std. dev: normalcdf: (LOW, HIGH, , ) If x > #: E99 as High If X < #: -E99 as Low

To find z-scores when given cumulative probabilities: Invnorm: (enter probability as decimal)You are given an area (probability) and asked to find the corresponding point (value). To find an x-value given percent wanted, mean, Std. Dev.: Invnorm: (% wanted, mean, Std. Dev.)

Central Limit Theorem: Just like #1, except n > 1Normalcdf: (Low, High, , )OrinvNorm: (Area to Left, , ) When n > 1 input- normalcdf (low, high, , /n)Normal as approximation to binomialStep 1: Using binomial formulas, find mean and standard deviation.Step 2: If you are asked to find Then in calculatorP(at least x) normalcdf(x-.5,1E99,,)P(more than x) normalcdf(x+.5,1E99,,)P(x or fewer) normalcdf(-1E99,x+.5,,)P(less than x) normalcdf(-1E99,x-.5,,)

Chapter 7 Estimates and Sample Sizes

Confidence Intervals: Mean: is known: ZInterval Unknown use: TIntervalZ-interval: (, Mean, n, C-Level)T-interval: (Mean, Sx, n, C-Level)Proportion- PropZint:

Chapter 8 Hypothesis TestingHypothesis Test Checklist___ CLAIM___ HYPOTHESES___ SAMPLE DATA___ ___ CALCULATOR: P-VALUE, TEST STATISTIC___ CONCLUSIONS

If P-Value < , reject H0; if P-Value > fail to reject H0. Z-Test: (o, , Mean, n, or ) T-Test: (o, Sx, Mean, n, or ) 1-PropZtest: (Po, x, n, prop p or )

Example: Z-Test to test claim: < 5.500, = 0.01, X= 5.497. s = 0.011, n = 36 Answer: p = .05 > , therefore, fail to reject Ho. There is not enough evidence at the 1% level to support the claim.

Sentence Statement/Final Conclusion Reject H0 (Type 1 reject true Ho) Claim is H0: There is sufficient evidence to warrant rejection of the claim that . . .Claim is H1: The sample data support the claim that . . .

Fail to reject H0 (Type II fail to reject false Ho) Claim is H0: There is not sufficient evidence to warrant rejection of the claim that . . . Claim is H1: There is not sufficient sample evidence to support the claim that . . .

Chapter 10 Correlation and Regression Diagnostic OnProblems: Enter data in L1 & L2 and find out if there is any correlation between X & Y. You can create a scatterplot w/ the data to visually see any +/- correlation. With correlation, you might be asked to make a prediction of Y when given X.X= Explanatory VariableY= Response VariableEnter raw data into a list: LinReg (ax + b) L1 for x, L2 for yEnter

LinRegTTest (Xlist: L1 & Ylist: L2 Freq: 1, 0) *Answer = r

LinReg:y = ax + b Wherea = 11.8244078 a Slopeb = 35.30117105 b y-interceptr2 = .9404868083 r2=coefficient determinationr = .9697869912 r= correlation coefficient