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FQ10
Formula quiz 10
| Question | Answer |
|---|---|
| point estimate | a single number used to estimate a population parameter |
| confidence interval | although a point estimate can be a reasonable approximation of a populatin parameter it is often safer to find an interval into which a parameter could fall |
| onfidence intervgals are intervals in the form of | point estimate plus or minus margin of error |
| a one sample z interval | it is used to estimate a populaton mu wehen the population standard deviation is known |
| the formula for a one sample z interval is | xbar plus or minus zstar times sigma over root n |
| 90% CI, z* is | 1.645 |
| 95% CI, z* is | 1.96 |
| 99% CI, z* is | 2.58 |
| assumptions fo rusing the formula for a one sample z interval | 1) an SRS 2) sigma is known 3) either the sample size is larger than 30 or it's normally distributed |
| 95% confidence means | f we constructed a 95% confidence interval using every possible sample of the same size, the true population mean would lie in 95% of these intervals |
| the margin of error in in a confidence interval is | the part of the formula that lies in back of the plus minus |
| make the margin of error smaller is | we use a larger samole size or a lower confidence level |
| the smaller the confidence level | the smaller, narrow, the confidence interval, asuming that the sample size is the same |
| msot of the time sigma is unknown, in large samples | we may use s, the sample standard deviation, in place of sigma |
| steps used to confudct a test of significane | 1) assumptions 2) null/alt hyp 3) calculate test statistic 4) calculate the pvfalue of the test statistic 5) interpret the results of the test (fail to reject, reject) |
| null hypothesis | the statement that claims that there is no change in the population |
| alternate hypothesis states | that whatever process wwe are testing has had an effet on the population |
| the pvalue of a significane test | is the porbability computed assuming that HO is true that the test statistic would tkake a value as extreme or more extreme than that actaully observed, the smaller the pvalue is the stronger the evidence against HO provided by the data |
| if the pvalue is lessthan alpha | we say tat our data is statisticall significant at this level and reject the null hypothesis |
| the test statistic for a one sample z test is | xbar minusmu over sigma over root n |
| assumptions for a one sample z test | 1) the population standard dev is known 2) srs 3) either the sample is large or the population is approvimately normal |
| if H0 is true and you reject Ho | type 1 error |
| if HO is true and you fail to reject HO | then it's the corect decision |
| if HA is true and you reject HO | it's the correct decision |
| if HA is true and you fail to reject HO then | it's a type 2 error |
| if asignificance test has a fixerd significane level of slpah then alpha | is the probability of making a type 1 error |
| the probability of a type 2 error is denoted by | the symbol beta |
| the probability that a fixed level alpha significance test will rejct ho when a particular alternative of the parameter is true | is called the power of the test against that alternative |
| the power of the test is the proabbility that the nll hypothesis | will be rejected if it is false |
| power of the test equals | 1-prob (type 2 error)= 1- B |
| there are two ways to increase the power of a significance test | a) increase the sample size b) increase the significance level |
| increasing the significance level increases | the probability of making a type 1 error which, in turn, dcreases the probability of making a type 2 error, which amkes 1- B a larger quantity |
Created by:
lilee256