Chapter 10
Statistical Inferences- acquires info & draw conclusion about population samples
Estimation- value of population parameter of sample statistic
Sample mean (x ) and estimate population mean (μ)
2-Types of estimator
1) Point Estimator- value of unknown parameter using SINGLE VALUE
- do not reflect larger sample size or parameter value
2) Interval Estimator (confidence interval)- RANGE OF VALUE unknown parameter using intervals,
lower/upper confidence limit w/ level of confidence
Qualities of Estimators- unbiased, consistency, relative efficiency
Unbiased estimator- expected value is equal to parameter E(x ) = μ (cant tell how close to parameter)
Consist estimator- difference btwn estimator & parameter grows smaller as sample gets larger
Relative Efficient estimator- 2 unbiased, 1 variance smaller is relative efficient
-larger confident level produces wider confidence intervals
-larger value of “σ” produce wider confidence intervals
-larger sample size, narrow confidence interval
-interval too wide increase sample size
Chapter 11
Non-statistical Hypothesis
1) Null Hypothesis- Ho: goes against what trying to prove (ex: defendant innocent)
2) Alternative (research) Hypothesis- H1: trying to prove something (ex: defendant guilty)
Type 1 Error reject H0 true null hypothesis, most serious “α” (convict innocent person)
Type 2 Error do not reject H0 false hypothesis “β” (ex: defendant not guilty acquitted)
1-Tail Test- greater than or less than (α)
2-Tail Test- between or equal too (α/2)
Critical Concepts
1) 2-Hypothesis: null & alternative
2) Assumption begins that null hypothesis true
3) Whether there is enough evidence to infer alternative hypothesis is true
4) 2-Decisions: (1) Is there enough evidence to support alternative hypothesis?
(2) Is there not enough evidence to support alternative hypothesis?
5) 2-Errors: Type 1 or Type 2
P-Value
Overwhelming Evidence- p-value less than 1% (highly significant)
Strong Evidence- p-value between 1-5% (significant)
Weak Evidence- p-value between 5-10% (not significant)
No Evidence- p-value exceeds 10% (not significant)
If p-value is smaller than Reject the null hypothesis.
The smaller the p-value, the more evidence to support the alternative hypothesis.
Decreasing significance level , increases the value of . |
Increasing sample size n, the value of will decrease. n
Decreasing sample size decreases test-stat & increase p-value. n - z p t
power of a test is defined as 1– P (reject null hypothesis when it’s false)