Chapter 1 Statistics, Data, and Statistical Thinking

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Chapter 1 Statistics, Data, and Statistical
Thinking

• Statistics the science of data.
• Statistical methods Descriptive
  Statistics(collecting data, presenting data,
  characterizing data), Inferential
  Statistics(Estimation, Hypothesis testing)
• Population, sample
• Quantitative data, Qualitative data

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Chapter 1 Statistics, Data, and Statistical
Thinking

• Data Sources(published source, designed
  experiment, survey, observational study)
• Random sampling(representative, equally likely to
  be selected)
• Sources of Error in Survey Data(Selection bias,
  Nonresponse bias, Measurement error)

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Chapter 2 Methods for Describing Sets of Data

• Graphical methods qualitative data (bar graph,
  par chart) quantitative data(dot plot,
  stem--leaf, histogram)
• Summation
• Central tendency(mean, median, mode)
• Shape left-skewed(meanltmedianltmode)
  symmetric(meanmedianmode) right-skewed(modeltmed
  ianltmean)

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Chapter 2 Methods for Describing Sets of Data

• Variability
• Range Largest measurement minus the smallest
  measurement
• sample variance
• Sample standard deviation(s)the positive
  square root of the sample variance

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Chapter 2 Methods for Describing Sets of Data

• Chebyshevs rule and Empirical rule
• pth percentile(25th 50th 75th percentile)
• Z-score
• Outliers box plots z-score.

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Chapter 3 Probability

• Events, sample space and probability
• Probability of an event the sum of the
  probabilities of all sample points in the
  collection for the event
• Combination rule

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Chapter 3 Probability

• Intersection
• If A and B are independent events
• Unions
• Complementary Event

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Chapter 3 Probability

• Mutually Exclusive Events
• Conditional probability
• Events A and B are independent

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Chapter 3 Probability

• Bayess rule
• where
  j1,,k

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Chapter 4 Discrete Random Variables

• Two types of Random Variable (discrete,
  continuous)
• 2 Requirements for discrete random variables
• Mean
• variance
• standard deviation

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Chapter 4 Discrete Random Variables

• Binomial
• Mean
• Variance
• Standard deviation

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Chapter 5 Continuous Random Variables

• Probability areas under curve
• and
  
• Uniform pdf c ? x ? d
• 
  c ? a lt b ? d
• Mean
• Standard deviation

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Chapter 5 Continuous Random Variables

• Normal
• Standard normal ? 0 and ? 1
• use normal table to get P(cltzltd)?
• Normal Convert to standard normal using

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Chapter 5 Continuous Random Variables

• Approximation of a binomial distribution
• 1. Calculate the interval
• If interval lies in rang 0 to n, normal
  approximation can
• be used
• 2. Express binomial probability in form
• or
• 3. For each value, a, use
• 4. Use standard normal table to find probability

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Chapter 6 Sampling Distributions

• Concept Parameter, Sample Statistic, Sampling
  distribution
• Sampling Distribution of
• Mean of sampling distribution equals mean of
  sampled population
• Standard deviation of sampling distribution
  equals
• Standard deviation of sampled
  population Square root of sample
  size

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Chapter 6 Sampling Distributions

• Central Limit Theorem
• In a population with standard deviation ?
  and mean ? , the distribution of sample means
  from samples of N observations will approach a
  normal distribution with standard deviation of
  and mean of as N gets
  larger (n ?30).

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Chapter 7 Inferences Based on a Single Sample
Estimation with Confidence Intervals

• Concept confidence interval, Confidence
  coefficient(1 - ?) , Confidence level
• Confidence Interval for ?
• known ?
• Unknown ?
• large sample n ? 30,
• small sample n lt 30,
• t?/2 on n-1 degrees
  of freedom

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Chapter 7 Inferences Based on a Single Sample
Estimation with Confidence Intervals

• Confidence interval for proportion p
• Sample statistic of
• Mean of sampling distribution of is p
• Standard deviation of the sampling
  distribution is where
  q1-p
• For large samples, the sampling distribution
  ofis approximately normal

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Chapter 7 Large-Scale Confidence Interval for a
Population Proportion

• Sample size n is large if falls
  between 0 and 1
• Confidence interval is calculated as
• where and
• X of successs

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Chapter 7 Inferences Based on a Single Sample
Estimation with Confidence Intervals

• Determining the Sample Size
• Sampling Error (SE), which is half the width
  of the confidence interval
• To estimate ? with Sampling error SE and
  100(1-?) confidence,
• where ? is estimated by s or R/4. Rounding
  the value of n obtained upward to ensure the
  sample size

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Chapter 7 Inferences Based on a Single Sample
Estimation with Confidence Intervals

• Sample size can also be estimated for population
  proportion p
• If pq is unknown you can be estimated by using
  .
• If pq is unknown and has no information about ,
• using p .5 since the value of pq is at its
  maximum
• when p .5

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Chapter 8 Inferences Based on a Single Sample
Tests of Hypothesis

• 7 elements
• The Null hypothesis H0 ?, ?, or ??
• The alternate, or research hypothesis Ha
  ?,??, or ?
• The test statistic
• The rejection region
• The assumptions
• The Experiment and test statistic calculation
• The Conclusion

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Chapter 8 Large-Sample Test of Hypothesis about ?

• One-Tailed Test
  Two-Tailed Test
• H0
  H0
• Ha (or Ha )
  Ha
• Teat Statistic
  Test Statistic
• 1. Rejection region
  Rejection region
• (or when )
• 2. Rejection region
  Rejection region
• (or when )

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Chapter 8 Small-Sample Test of Hypothesis about

• One-Tailed Test
  Two-Tailed Test
• H0
  H0
• Ha (or Ha )
  Ha
• Teat Statistic
  Test Statistic
• 1. Rejection region
  Rejection region
• (or when )
• 2. Rejection region
  Rejection region
• (or when )
• where t? and t?/2 are based on (n-1) degrees of
  freedom

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Chapter 8 Large-Sample Test of Hypothesis about a
Population Proportion
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Chapter 9 Inferences Based on Two Samples
Confidence Intervals and Tests of Hypothesis

• Comparing Two Population Means Independent
  Sampling
• Large Sample Confidence Interval for ?1 - ?2

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Chapter 9 Comparing Two Population Means
Independent Sampling

• Large Sample Test of Hypothesis for ?1 - ?2

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Chapter 9 Comparing Two Population Means
Independent Sampling

• Small Sample(n1 lt 30, n2 lt 30 )Confidence
  Interval for ?1 - ?2 (assume
  )
• where
• pooled estimated of
• and t?/2 is based on (n1 n2-2) degrees of
  freedom

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Chapter 9 Comparing Two Population Means
Independent Sampling

• Small Sample Test of Hypothesis for ?1 - ?2

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Chapter 9 Comparing Two Population Means
Independent Sampling

• Small Samples what to do when
• When sample sizes are equal (n1n2n)
• Confidence interval
• Test Statistic for H0
• where t is based on
  degrees of freedom

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Chapter 9 Comparing Two Population Means
Independent Sampling

• Small Samples what to do when
• When sample sizes are not equal (n1?n2)
• Confidence interval
• Test Statistic for H0
• where t is based on
  degrees of
• 
  freedom
• Round down to the nearest integer

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Chapter 9 Comparing Two Population Means Paired
Difference Experiments

• Paired Difference Confidence Interval for ?d?1 -
  ?2
• Large Sample
• (nd?30)
• Small Sample
• (ndlt30)
• where t?/2 is based on (nd-1) degrees of freedom

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Chapter 9 Comparing Two Population Means Paired
Difference Experiments

• Paired Difference Test of Hypothesis for ?d?1 -
  ?2, Large Sample

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Chapter 9 Comparing Two Population Means Paired
Difference Experiments

• Paired Difference Test of Hypothesis for ?d?1 -
  ?2, Small Sample

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Chapter 9 Comparing Two Population Proportions
Independent Sampling

• Large-Sample(both intervals,
• and , fall between 0 and 1)
  100(1-?) Confidence Interval for (p1-p2)

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Chapter 9 Comparing Two Population Proportions
Independent Sampling

• Large-Sample Test of Hypothesis about (p1-p2)

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Chapter 9 Determining the Sample Size

• For estimating ?1-?2 (assuming n1n2n)
• 
  (rounding up)
• These estimates of and might be
  sample variance and from prior
  sampling, or based on the range sR/4.
• For estimating p1-p2 (assuming n1n2n)

These estimates of and might be
based on prior samples, or for guess
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Chapter 11 Simple Linear Regression

• Model
• Least Squares Line
• Slope y-intercept

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Chapter 11 Model Assumptions

• Mean of the probability distribution of e is 0
• Variance of the probability distribution of e is
  constant for all values of x
• Probability distribution of e is normal
• Values of e are independent of each other

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Chapter 11 Simple Linear Regression

• Estimator of ?2
• sampling distribution of
• We estimate by

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Chapter 11 Simple Linear Regression
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Chapter 11 Simple Linear Regression

• A 100(1-a) Confidence Interval for ?1
• where
• Coefficient of Correlation r
• Coefficient of Determination r²

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Chapter 11 Using the Model for Estimation and
Prediction

• 100(1-a) Confidence interval for Mean Value of y
  at xxp
• 100(1-a) Confidence interval for an Individual
  New Value of y at xxp
• where ta/2 is based on (n-2) degrees of freedom

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Chapter 13 Testing Category Probabilities
One-Way Table

• Ha at least one of the multinomial probabilities
  does not equal its hypothesized value
• Test statistic
• where is the expected cell
  count.
• Rejection region
• where has (k-1)df

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Chapter 13 Testing Category Probabilities
Two-Way (Contingency) Table

• Used when classifying with two qualitative
  variables
• H0 The two classifications are independent
• Ha The two classifications are dependent
• Test Statistic
• Rejection region?2gt?2?, where ?2? has (r-1)(c-1)
  df