Statistics - 3

Statistics - 3

1. Confidence Interval: x bar +- z* (sigma/root n)

   • Confidence Levels: 90%=1.645, 95%=1.96, 99%=2.575
   • Margin of error: m=z*(sigma/root n)
     • Higher confidence = larger margin of error
     • Margin of error gets smaller when z* gets smaller, sigma is smaller, n gets larger
       • Larger sample size = smaller SD (Spread), spread decreases at rate = root n
     • To find sample size: n=(z*sigma/m)^2

2. Hypotheses (Null & Alternative)

   • One-sided: EITHER smaller or larger
   • Two-sided: parameter is DIFFERENT from null
   • Test statistic: measures how far the data diverge from expected if null is true
     • z=(estimate-hypothesized value)/sd of estimate
     • P-value < alpha -> reject null, conclude alternative. P-value >= alpha -> fail to reject null -> cannot conclude alternative
     • Tests of Significance: 1. State null and alternative hyp. 2. Test statistic 3. Find p-value 4. Conclusion
       • Hypothesis testing: 1. Determine correct test 2. Hypotheses 3. Collect data 4. Ensure conditions hold 5. Test statistic 6. P-value 7. CI matching level of significance 8. Conclusion
     • One-sample z-statistic: z= (x bar - mu)/sigma/root n). Inference for unknown population mean, sd is known
       • T-test: t=(x bar-mu)/(sigma/root n). SAME AS Z STAT. Used when sd is unknown
         • CI= x bar +- tn-1(8/root n)
         • degrees of freedom = n-1
         • T-distribution table: Top: area in upper tail... (area x 2) - 1 -> CI. Left: df Intersection: t-stat
         • Matched Pairs Test: comparing means of 2 dependent population means
           • x bar d= x bar before - x bar after. mu d=difference between means - usually 0. Continues with usual t-test
         • Difference of 2 Means: Comparing means of 2 independent populations
         • Pooled 2 sample t-test: used when variability is appox. equal
     • Two sided: For two-sided, confidence interval can be used: C=1-alpha

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