Show Recommended textbook solutions
 Statistical Techniques in Business and Economics15th EditionDouglas A. Lind, Samuel A. Wathen, William G. Marchal 1,236 solutions
The Practice of Statistics for the AP Exam5th EditionDaniel S. Yates, Daren S. Starnes, David Moore, Josh Tabor 2,433 solutions
Mathematical Statistics with Applications7th EditionDennis Wackerly, Richard L. Scheaffer, William Mendenhall 3,341 solutions
Understandable Statistics: Concepts and Methods12th EditionCharles Henry Brase 3,169 solutions Recommended textbook solutions
The Practice of Statistics for the AP Exam5th EditionDaniel S. Yates, Daren S. Starnes, David Moore, Josh Tabor 2,433 solutions
The Practice of Statistics for AP4th EditionDaniel S. Yates, Daren S. Starnes, David Moore 2,491 solutions
Mathematical Statistics with Applications7th EditionDennis Wackerly, Richard L. Scheaffer, William Mendenhall 3,341 solutions
Statistics for Business and Economics8th EditionBetty Thorne, Paul Newbold, William Carlson 1,292 solutions
Terms in this set (28)Logic of Statistical Comparison of Two Populations In order to guess a population mean (to be able to do hypothesis testing), it can help to make inferences about two population means and ask if the two population means differ. Naturally Occurring Population a population that is present without any intervention by the investigator Hypothetical Population the observations don't exist until they are actually
measured Independent Samples two or more random samples are independent when the scores included in one random sample are unrelated to the scores included in the other random sample Dependent Samples two or more random samples are dependent when the scores included in one random sample are systematically related to the scores included in another random sample Sampling Distribution of the Difference Between Sample Means (Independent Samples) Null hypothesis: μ1-μ2=0 (no difference between two population means) Test statistic: t statistic based on M1-M2 Sampling distribution of M1-M2
characteristics: Standard Error of the Sampling Distribution of M1-M2 (but just 1 value for σ ) Estimate of the Standard Error, s(M1-M2) -used to compute the t statistic for independent samples Pooled Variance the weighted average of s1² and
s2² The t Distribution for Independent Samples convert the sampling distribution of M1-M2 into the distribution of the t statistic so we can use tabled values Characteristics: T Statistic for Independent Samples -compute pooled variance Hypothesis Testing with the Sampling Distribution of the Independent Sample t Statistic Goal: determine whether the means of 2 populations are the same or different 1. Make sure assumptions are met Assumptions of Independent-Sample t Test if these assumptions can't be met, use the rank-sum test Hypotheses of Independent Sample t Test Null Hypothesis: must propose a specific value for μ1-μ2 (the mean of the sampling distribution of M1-M2). The symbol for the difference is Δ0, and it's
typically 0. Alternative Hypothesis: proposes difference between population means is greater than, less than, or not equal to 0 (Δ0) Increasing Power of the Independent Sample t Test -increase alpha Calculating Power of Independent Sample t-Test 1. Propose an effect size based on a value for μ1-μ2. Either compute it or pick a standard value (.2, .5, .8) Given my alpha, sample size, and alternative hypothesis, what is the probability that I will reject the null if my proposal for the effect size is correct? 2. Compute 𝛿 Effect Size (d) Estimation requires guesses for σ (common population variance) and a specific difference for the difference between the population means (Δs) d= |Δs-Δ0|/σ 𝛿 Formula 𝛿= d√(n1)(n2) / (n1+n2) Sample Size Analysis for Independent Sample t Test 1. Specify desired power Given my alpha and type of alternative hypothesis, what sample size do I need to obtain the desired power if my estimate of the effect size is correct? 3. Find in the table the 𝛿 corresponding to the alpha and alternative and power you're looking for N formula n= 2(𝛿/d)² Estimating the Difference Between Two Population Means The statistic M1-M2 is an unbiased point estimator for μ1-μ2, but it's probably not exact, so interval estimation is the way to go. 1. Make sure assumptions are met (relatively normal distribution, same population variance or sample size, the samples are independent of one another, independent random sampling was used,
interval or ratio data) Confidence Interval Formula Upper limit= M1-M2 + (s{M1-M2} x t{α/2}) The Rank-Sum Test for Independent Samples Nonparametric procedure that corresponds to the independent-sample t test; used to compare 2 populations when 2 independent samples from them are available. When assumptions for independent sample t test are grossly violated, you have to resort to this nonparametric test. Doesn't require any assumptions about the population distributions, so the test is less powerful and the null is less specific (so you don't know exactly how the samples differ if it's rejected) The Rank-Sum Statistic, T How to compute the T Statistic: When the null hypothesis is correct (the two populations have the same distributions), then both the high and low ranks should be equally distributed across the two samples. If the null is incorrect, the one of the samples should have higher scores and the other should have lower, so the T is one sample will be higher than the other. To determine whether or not the null is correct, we determine if the T statistic is very large or very small by comparing it to the sampling distribution of the statistic. Sampling Distribution of the T Statistic When the two sample sizes are both more than 7 and the null is correct, When the null is correct, then the T from the sample will be approximately equal to μT, and the z score will be close to 0 When the null is incorrect, then T will be much larger or smaller than μT, and z will be much larger or smaller than 0 Hypothesis Testing Using T 1. Make sure assumptions are met Assumptions of Rank-Sum T Test 1. The two samples are independent Hypotheses of Rank-Sum T Test Null: H0: the two populations have identical relative frequency distributions Nondirectional Alternative: H1: the two populations do not have identical relative frequency distributions Directional Alternative: H1: the scores in Population 1 tend to exceed the scores in Population 2 Sets with similar termsCommunications Research Methods67 terms Taylore44 STATS 119 FINAL SDSU87 terms thomasmicha11 Chapter 10 Part 210 terms JacobEvans_ TOM 30219 terms Alma_Garcia31 Sets found in the same folderCh. 17: Comparing Multiple Population Means: One-F…13 terms allie_adamis Ch. 18: Introduction to Factorial Designs9 terms allie_adamis Ch. 1: Why Statistics?22 terms allie_adamis Ch. 2: Frequency Distributions and Perce…31 terms allie_adamis Other sets by this creatorSun Salutation Poses10 terms allie_adamis Anatomy18 terms allie_adamis Greek Basic Vocab43 terms allie_adamis Round 2196 terms allie_adamis Verified questions
QUESTION A small class of five statistics students received the following scores on their AP Exam: 5, 4, 4, 3, 1. Calculate the mean and standard deviation of these five scores. Verified answer
STATISTICS An airline does a market research survey on travel patterns. It takes a simple random sample of 225 people aged 18 and over in a certain city, and works out the 95%-confidence interval for the average distance they travelled on vacations in the previous year. This was 448 to 592 miles. Say whether each statement below is true or false; give reasons. If there is not enough information to decide, explain what else you need to know. a) The average of the 225 distances is about 540 miles. b) The SD of the 225 distances is about 390 miles. c) The histogram for the 225 distances follows the normal curve. d) The probability histogram for the sample average is close to the normal curve. e) The probability histogram for the population average is close to the normal curve. f) A 95%-confidence interval based on sample of 450 people will be about half as wide as one based on a sample of 225 people. Verified answer STATISTICS A simple random sample of size n is drawn from a population that is known to be normally distributed. The sample variance, $s^2$, is determine to be 19.8. (a) Construct a 95% confidence interval of $\sigma^2$ if the sample size, n, is 10. (b) Construct a 95% confidence interval for $\sigma^{2}$ if the sample size, n, is 25. How does increasing the sample size affect the width of the interval? (c) Construct a 99% confidence interval for $\sigma^2$ if the sample size, n, is 10. Compare the results with those obtained in part (a). How does increasing the level of confidence affect the width of the confidence interval? Verified answer
PROBABILITY Assume that the chest measurements are normally distributed with a mean of $\mu$=39.83 and standard deviation of $\sigma$=2.05. a. What proportion of the observations would lie between 36.5 and 43.5 inches? b. Between what two measurements would 95% of the observations lie? c. What are the actual proportions for parts a and b using the data directly Comment on the accuracy of the proportions found using assumed normality of the chest measurements. Verified answer Recommended textbook solutionsThe Practice of Statistics for the AP Exam5th EditionDaniel S. Yates, Daren S. Starnes, David Moore, Josh Tabor 2,433 solutions
The Practice of Statistics for the AP Exam6th EditionDaren S. Starnes, Josh Tabor 2,673 solutions
Statistics for Business and Economics8th EditionBetty Thorne, Paul Newbold, William Carlson 1,292 solutions
Graphing Calculator Manual with Elementary Statistics11th EditionMario F. Triola 2,879 solutions Other Quizlet setsSIOP Strategies 1-1540 terms Jessie_Hagen Personal Need for Structure (PNS)29 terms confuzzled_always AQA Biology 9-1 - Homeostasis and Respon…33 terms sagemel Lecture 3 + 428 terms rupinder13 Related questions
QUESTION Which criterion does an experimenter use to decide whether to accept or reject the null hypothesis? 12 answers QUESTION What are the degrees of freedom for the independent samples t-test? 15 answers QUESTION what is the main advantage of a contrived observation (compared with other types of observational research)? 8 answers QUESTION What are the 3 pillars of evidence? 15 answers How do you perform a twoSteps to Calculate Two Sample T Hypothesis Test (Equal Variance). State the claim of the test and determine the null hypothesis and alternative hypothesis.. Determine the level of significance.. Calculate degrees of freedom.. Find the critical value.. Calculate the test statistics.. How do you do a twoTwo Sample t-test: Example. Step 1: Gather the sample data. Suppose we collect a random sample of turtles from each population with the following information:. Step 2: Define the hypotheses. ... . Step 3: Calculate the test statistic t. ... . Step 4: Calculate the p-value of the test statistic t. ... . Step 5: Draw a conclusion.. What test can be used to test the difference between two sample means when the population variances are known?An F-test (Snedecor and Cochran, 1983) is used to test if the variances of two populations are equal. This test can be a two-tailed test or a one-tailed test. The two-tailed version tests against the alternative that the variances are not equal.
What does the tA t-test is an inferential statistic used to determine if there is a significant difference between the means of two groups and how they are related. T-tests are used when the data sets follow a normal distribution and have unknown variances, like the data set recorded from flipping a coin 100 times.
|
