ECON 203 1nd EditionExam # 1 Study Guide Lectures: 1 - 11Lecture 1 (August 27)Syllabus Review- Office HoursRoom 116 David Kinley HallWed 10:15 – 11:15- Required- Homework every week on compass- Textbook paperback or online- Projects and exams- Everything is in notes package pages 1-5 Introduction to Economics 203 Statistics“Without data, ours is just another opinion” Utilize data to conduct scientific analysis thereby informing judgment“Tool Chest”Objectives- Describe a single population- Compare two or more populations- Analyze the relationship between two or more variables- Forecast value Data types- Quantitative data- Qualitative data- Time series data- Cross-sectional dataOverview of Economics 203- Understand the relevance of statistics in future courses and work environments- Built off of the basis of Economics 202Homework- On Aplia, look at course packet for help- Reference notes for clarification- Office Hours helpsLecture 2 (August 29)Confidence Interval Estimation- Point estimates include: “u”, standard deviation, “s” “p” etc.Formulas:Standard Error … for Population Mean w/Sigma known= (standard dev./square root of “n”)Population mean w/Sigma unknown= (s/square root of “n”)Population Proportion = square root of (p(1-p)/”n”)Margin of Error…For Population Mean w/Sigma known = z+or- standard dev./square root of “n”Get used to using the formula sheet in the back of the notes package so that when we have an exam you will be used to referring to that sheetExample on slide 26 of notes package:Answer  1-a = .90 a = .10 a/2 = .05 95% : 1-a = .95 a = .05 a/2 = .025Z.025 = 1.96 Example on slide 29 of notes package:Answer  n = 70 s = $24,000 average = $856,000 standard dev. = $28,00010% significance level [850000 . 861000] Rounding: Always round “n” up, e.g. calculate 84.2 up to 85 Example on slide 33 of notes package: Answer  n = 49 standard deviation = .78 average = 32.6It’s a “z” distributing because the standard deviation is known95% confidence interval: 32.6+/-1.96(.78/square root of 49) = [32.3816, 32.8184]99% confidence interval: 32.6+/-2.58(.78/square root of 49) = [32.3125, 32.8875]Lecture 3 (September 3)Confidence Interval EstimationPoint estimates include: “u”, standard deviation, “s” “p” etc.Formulas:Standard Error …For Population Mean w/Sigma known= (standard dev./square root of “n”)Population mean w/Sigma unknown= (s/square root of “n”)Population Proportion = square root of (p(1-p)/”n”) Margin of Error…For Population Mean w/Sigma known = z+or- standard dev./square root of “n” Get used to using the formula sheet in the back of the notes package so that when we have an exam you will be used to referring to that sheetExample on slide 26 of notes package:Answer  1-a = .90 a = .10 a/2 = .05 95% : 1-a = .95 a = .05 a/2 = .025Z.025 = 1.96Example on slide 29 of notes package:Answer  n = 70 s = $24,000 average = $856,000 standard dev. = $28,000 10% significance level [850000 . 861000] Rounding: Always round “n” up, e.g. calculate 84.2 up to 85 Example on slide 33 of notes package: Answer  n = 49 standard deviation = .78 average = 32.6It’s a “z” distributing because the standard deviation is known95% confidence interval: 32.6+/-1.96(.78/square root of 49) = [32.3816, 32.8184]99% confidence interval: 32.6+/-2.58(.78/square root of 49) = [32.3125, 32.8875]Lecture 4 (September 5)Aplia Homework 2Hypothesis Testing, Example 12Relevant point estimate- This variable is found by taking the number of customers who purchased the glass and divide it by the total- 151/950 = .1589 … = .159Value of Test Statistic- Use the “z” variable equation- P = .15 because that is the population standard- Z = (p-hat – p)/ sqrt((p(1-p))/n)- Z = (.159 - .15)/sqrt((.15*.85)/950) = .7723P-value- All tests about proportion use a z statistic, so this test statistic follows a standard normal distribution- In excel put =NORMSDIST(z) . This will return the area to the left of “z”- NORMSDIST(.7723) = .7800 …. 1-.7800 = .2200Type I error conclusion- Allowing for a 5% chance of error- Which means that 95% of the experiment must be correct in order for the company to pursue this line of cartoon mugs- Do not reject the null hypothesis, and conclude that there is insufficient evidence that the special offer should be introduced- The p-value is not less than alpha=.05, therefore conclude that there is insufficient evidence that the special offer should be introducedLecture 5 (September 8)Statistical Inference: Single Population VarianceWill always be one data setWhen to use variance:Wanting to find consistence of a productionAssessing risk of investmentTransformationS^2 becomes X^2 through the formula ((n-1)*(s^2))/(standard dev^2)Takes us from sample distribution to standardized distributionChi-SquaredLooks like X^2Non negative distributionThe number in the bottom right corner of chi-squared is always on the right side of the distribution graphExample on slide 8 page 46Do not reject null hypothesis because insufficient evidence to prove alternativeP-ValueAlways the area on the graph between chi-squared and the end of the rejection region.Example on slide 11 page 48(19*5.7)/4.0 = 27.075Chi-squared.05,19 = 30.14353Do not reject H0 Insufficient evidenceLecture 6 (September 10)Statistical Inference: Two Population Mean, Proportion & VarianceSingle PopulationX²  Does Obama have majority support? Is this stock risky?Case 1: The two population variance values are known (pg. 52)Facts about paragraph #1- Of independent population 2 formula- “Previous studies” = we know this is true- Since standard deviations are known, then the variance is also known- Since there is no matching, it must be independentFacts about paragraph #2- Always assume 95% confidence when it’s not statedGoing Through Phaseso Ho: u1 = u2, Ha: u1 ≠u2o Z = 3.876o Z.025 = 1.96o Reject Ho, we have proven that the number of days differ between citiesLecture 7 (September 12)Statistical Inference: Two Population Difference in Means- Always assume variances are equal unless it is specified otherwiseCase 1The excel table- Mean = x- Observations = n- Pooled Variance = S²- U1 – U2 = 0Case 2Tail Test- Use one sided test because it’s one tailed, so it’s t.05 but when using confident