Download Factors Influencing Confidence Intervals - Review Sheet | STAT 200 and more Study notes Statistics in PDF only on Docsity! x t s nn d f ± −α/ , . .2 1 STAT 200 Review Sheet FACTORS INFLUENCING CONFIDENCE INTERVALS Confidence Interval for the Mean x z s n ± α/2 Confidence Interval for a Proportion p z pq n ± α/2 FACTOR FACTOR WHEN FACTOR GETS SMALLER REASON EXAMPLE n sample size C.I. gets larger Smaller sample size means a larger standard error and less certainty 25/50 = 3.54 25/500 = 1.12 Type I error C.I. gets larger If you accept smaller Type I error, i.e., the probability that a C.I. will not contain the mean, you have to allow for a larger C.I. to be that sure Z.05/2 = 1.96 Z.01/2 = 2.575 1- % C.I. C.I. get smaller A smaller % C.I. means you are willing to accept more Type I error, so we can have a tighter C.I. 95% C.I. uses Z.05/2 = 1.96 99% C.I. uses Z.01/2 =2.575 or s Std Dev of Population; Std Dev of sample C.I. gets smaller If the population has less variability the sampling distribution will also have less variability 25/50 = 3.54 5/50 = .71 FACTORS INFLUENCING A HYPOTHESIS TEST Test Statistic for a Mean ( ) ( ) ( ) ( )z x s n or t x s n o o* / * / = − = −µ µ Test Statistic for a Proportion Note: Po comes from the Null Hypothesis ( ) z p p p q n o o o * = − FACTOR FACTOR WHEN FACTOR GETS SMALLER REASON EXAMPLE n Sample size Test Statistic gets smaller Smaller sample size means larger standard error. Tthe denominator of the test statistic will be larger, and z* or t* will be smaller 25/50 = 3.54 25/500 = 1.12 Type I error Test Statistic unchanged Rejection region z gets larger The rejection region gets larger making it more difficult to reject Ho Z.05/2 = 1.96 Z.01/2 = 2.575 One or 2- Tailed Test Nature of Alternative Hypothesis Test Statistic unchanged Rejection region z gets smaller with 1-tailed test With a one-tailed test, all of is put into the one tail Two-Tailed Z.05/2 = 1.96 One Tailed Z.05 = 1.645 or s Std Dev of Population; Std Dev of sample Test Statistic gets larger If the population has less variability, the sampling distribution has less variability, and denominator of the T.S. is smaller 25/50 = 3.54 5/50 = .71
