Inferential Statistics: Central Values and Confidence Intervals - Prof. Brian C. Dennis, Exams of Statistics

Download Inferential Statistics: Central Values and Confidence Intervals - Prof. Brian C. Dennis and more Exams Statistics in PDF only on Docsity! Inferences about central values ( ). ] µ normal , a b. 5# Inferences about using data: , , ..., (collected as a. C C C" # 8 random sample) Point estimate .s œ C œ C ) C )â) C+ 8 1 a b" # 8 How good is the estimate? Confidence interval ( known)5# A 100 1 % confidence interval (CI) for isa b+ ! . # $È È a bC + D C ) D œ 6 ?+ +8 8! !Î# Î#5 5, , A CI is constructed so that under repeated sampling, the long-run proportion of such intervals that contain will be.a b1 :+ ! P 1# $È È] + D 0 0 ] ) D œ ++ +8 8! !Î# Î#5 5. ! Š ‹What is PŠ ‹C + D 0 0 C ) D+ +! !5 5Î# Î#8 8È È. ? What does the estimate say about contending models? Statistical hypothesis tests ( known)5# First model: (known constant). .œ ! “Null hypothesis” H (often the skeptic's hypothesis)! One-sided in the other direction (left-tailed test) Hypotheses: H : ! !. .  H : a . .0 ! Rejection region (decision rule) reject H if ! D Ÿ + D! do not reject H if ! D 2 + D! Two-sided hypothesis test H : ! !. .œ H : a . .Á ! Rejection region: reject H if is outside of , ! +C C C+ ˆ ‰1 ! !# # Test statistic: D œ C+ + Î 8 . 5 !ˆ ‰È Rejection region: reject H if ! Î#k kD   D! do not reject H if ! Î#k kD 0 D! T -values for hypothesis tests The for a hypothesis test is the probability that,:-value under repeated sampling, the test statistic would be as extreme as the observed value of the test statistic, given that the null hypothesis is true. Right-sided: H : ! !. .Ÿ H : a . .2 ! : œ T ^   Da b reject H if reject H if ! !D   D Í : Ÿ! ! Left-sided: H : ! !. .  H : a . .0 ! : œ T ^ Ÿ Da b reject H if reject H if ! !D Ÿ + D Í : Ÿ! ! Two-sided: H : ! !. .œ H : a . .Á ! 2: œ T ^   Da bk k reject H if reject H if ! !Î#k kD   D Í : Ÿ! !