MATH 243 Study Guide - Final Guide: Random Variable, Interquartile Range, Categorical Variable
8 Jun 2018
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MATH 243 Final Study Guide
Chpt 18: Tests of Significance
• Following must be true in order to use the z procedures from Chpts 16 & 17 (both z based
confidence intervals and significance tests).
o Normally distributed
▪ Histogram of sample roughly symmetric, no outliers, clustered around center
o Pop. standard deviation is known
o SRS
• Margin of error for a confidence interval only accounts for error that occurs from
accidentally getting an unresponsive sample through valid sampling process. It does not
account for practical difficulties such as undercoverage and nonresponse.
• Possible errors for Sig Tests:
o Reject H0 when its true, Type I error (false positive)
o Fail to reject H0 when its true, Type II error (false negative)
o Power of test against Alt Hypothesis is probability that we reject null hypothesis
when false.
Chpt 20: Inference About a Population Mean
• 1 sample t test is a confidence interval or significance test for mean when sigma is
unknown. Guidelines:
o distribution is normal
o SRS
• Standard error of statistic is standard deviation of statistic estimated from data. SD of
sample mean is
• Test statistic:
• L level Confidence Interval for mu is given by
• Robustness of one sample T test (assuming we have an SRS)
o If n < 15, use t test if data appears to be close to normal
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MATH 243 Final Study Guide
o If 15 , use t test if data has at ost slight o odeate skeess
o If , use t test fo ay distiutio
Chpt 21: Two Sample t Tests
• Need following characteristics in order to get valid results:
o “R“’s
o both distributions Normal
o samples are independent
• Confidence interval for is given by
with degrees of freedom given by df = min(n1-1 , n2-1)
• Test Statistic:
• Assuming SRS, two sample t test will give valid results if:
o For n1 & n2 , distiutios ae siila i shape ad saple sizes ae aout the
same
▪ For n1+n2 < 15, distributions of both data sets should be roughly Normal
o Fo 1+n2 < 40, both data sets are slightly or moderately skewed but contain no
outliers.
o For n1+n2 , alost ay distiutios ae aeptale.
Chpt 22: Inference About a Population Proportion
• Instead of asking what the mean value of some population characteristic is, we can ask
what proportion of the population satisfies some condition.
o 8% of a lage letue psyh lass epots that they egulaly atted lass s The
ea attedae ate of a lage psyh lass is . letues pe eek
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MATH 243 Final Study Guide
• From SRS of size n, let p denote the actual population proportion of successes, &
sample proportion denoted phat =
• Use large-sample confidence intervals for p only when
o Nphat ,
o And n(1-phat) ad
o Population is at least 10x as large n
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Document Summary
Chpt 20: inference about a population mean: 1 sample t test is a confidence interval or significance test for mean when sigma is unknown. Guidelines: distribution is normal, srs, standard error of statistic is standard deviation of statistic estimated from data. Sd of sample mean is (cid:2201) (cid:2196: test statistic: (cid:2777) (cid:2201)/ (cid:2196, l level confidence interval for mu is given by (cid:1802)(cid:1801) (cid:2202) (cid:2201) (cid:2196, robustness of one sample t test (assuming we have an srs) If n < 15, use t test if data appears to be close to normal. If 15 (cid:1095) (cid:374) (cid:1095) (cid:1008)(cid:1004), use t test if data has at (cid:373)ost slight o(cid:396) (cid:373)ode(cid:396)ate ske(cid:449)(cid:374)ess. If (cid:374) (cid:1096) (cid:1008)(cid:1004), use t test fo(cid:396) a(cid:374)y dist(cid:396)i(cid:271)utio(cid:374) Math 243 final study guide: cluster = population divided into groups; clusters and then take srs of clusters to create sample (coffee company takes srs of 8 locations in pacific.
