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Midterm

QMS 202 Midterm: QMS 202 crib sheet 2

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Department
Quantitative Methods
Course
QMS 202
Professor
Clare Chua- Chow
Semester
Winter

Description
Confidence Interval: (INTR) – The true difference in means falls inbetween the confidence interval 2-Sample Z Interval - calculates the confidence interval for the difference between two population means when the population standard deviations of two samples are known. 2-Prop Z Interval - calculates the confidence interval for the difference between the proportion of successes in two populations. 2-Sample t Interval - calculates the confidence interval for the difference between two population means when both population standard deviations are unknown. 2-Sample Z TEST: 2-Propotion Z TEST: 2-Sample t TEST: C-Level: Confidence Interval = 1 – α C-Level: Confidence Interval = 1 – α LIST MODE: σ1: standard deviation of sample 1 x1: mean of sample 1 P1: =, σ2: standard deviation of sample 2 N1: sample size of 1 List1: List 1 x1: mean of sample 1 x2: mean of sample 2 List2: List 2 N1: sample size of 1 N2: sample size of 2 Freq1: 1 x2: mean of sample 2 ANSWER: Freq2: 1 N2: sample size of 2 Left: Left end of interval Pooled: Off ANSWER: Right: Right end of Interval ANSWER: Left: Left end of interval P1(with roof): point estimate of proportion Left: Left end of interval Right: Right end of Interval P2(with roof): point estimate of proportion Right: Right end of Interval P1(with roof): point estimate of proportion N1: Sample size 1 df: degree of freedom P2(with roof): point estimate of proportion N2: Sample size 2 x1: mean of sample 1 N1: Sample size 1 NOTE: the intervals can be turned around x2: mean of sample 2 N2: Sample size 2 so left could be right and right could be left sx1: NOTE: the intervals can be turned around so and they could both be positives even if it NOTE: the intervals can be turned around left could be right and right could be left and shows a negative make sure to put it into so left could be right and right could be left they could both be positives even if it shows a to question and see it makes sense and they could both be positives even if it negative make sure to put it into to question shows a negative make sure to put it into and see it makes sense to question and see it makes sense α = significance level Critical Value: (DIST) – STAT value ----------------- Critical Z value = Stat – Dist – Norm – InvN ------ Z value = + and - DIST – NORM – InvN DIST – t – Invt Tail: right, left , centre Area: 1 – level of significance for right or left tail test AND for two tail Area: percentage test 1 – level of significance/2 σ: standard deviation = 1 df: n – 1 (n = sample size) µ: = 0 ANSWER = – but the + and – of the answers is the non-rejection region between them and outside is the rejection region 𝑧_𝑠𝑐𝑜𝑟𝑒 = (𝑥−μ)÷𝜎 ----------- x = claim value, μ = population mean ,𝜎 = Standard deviation **If you need to find x find z score using InvN and plug the answer into the z score equation ** For a two tailed test answer = + and - OR for one tail left = - OR for one tail right = + Hypothesis Testing: (TEST) 2-Sample Z Test - tests the equality of the means of two populations based on independent samples when both population standard deviations are known. 2-Prop Z Test - tests to compare the proportion of successes from two populations. 2-Sample t Test - compares the population means when the population standard deviations are unknown. H0: µ or π = ≥ ≤ Ha: µ or π ≠ < > 2-Sample Z TEST: 2 indep POP σ known 2-Proportion Z Test: 2-Sample t Test: 2 indep POP σ equal but µ1: =, >, < P1: =, unknown, 2 indep POP σ unequal and σ1: standard deviation of sample 1 x1: mean of sample 1 unknown, 2 dep POP σ equal but unknown σ2: standard deviation of sample 2 N1: sample size of 1 -Normally distributed with the same variance x1: mean of sample 1 x2: mean of sample 2 -normally distributed with unequal variance N1: sample size of 1 N2: sample size of 2 µ1: =, >(higher/greater), < x2: mean of sample 2 ANSWERS: x1: mean of sample 1 N2: sample size of 2 P1: alternative hypothesis SX1: Standard deviation of sample 1 ANSWERS: Z: Z test statistic N1: sample size of 1 µ1: alternative hypothesis P: p value x2: mean of sample 2 z: z test statistic P1(with roof): sample proportion SX2: Standard deviation of sample 2 p: p value P2(with roof): sample proportion N2: sample size of 2 x1: mean of sample 1 P(with roof): pool propotion Pooled: ON x2: mean of sample 2 LIST MODE: N1: sample size of 1 Since p value is less than P1: =, N2: sample size of 2 -If p value is larger than α Do not reject H0 List1: List 1 -If p value is less than α reject H0 List2: List 2 1. Freq1: 1 F-Test: For testing the equality of two Z Stat = x(with mark on top) - µ ÷ (σ ÷ n Freq2: 1 variances – this tes
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