solved problems on hypothesis testing pdf

1. /Length 420 12 0 obj The main objective in statistics is testing a hypothesis. << /S /GoTo /D (Outline0.6) >> The DV is measured on an interval scale 2. Step 3 Compute the test value. A hypothesis test can be one-tailed or two-tailed. NOTE: To do the hypothesis test homework problems for this chapter and later chapters, make copies of the appropriate special solution sheets. Hypothesis testing is widely regarded as a valuable tool for data analysis but it is conceptually difficult to understand and even more difficult to carry out the procedure. This conjecture may or may not be true. 4. endobj *g#�)o�;u�0`��ve�qU'�,��X��m�S�؞Cu�Vf�Ȏ_�=~��mt׸�qn��!�f߽ٵ��&��}��_��!��>ň>:]�i[}�H(!S��N�$�W�. Chapter 7: Hypothesis Testing - Solutions 7.1 Introduction to Hypothesis Testing The problem with applying the techniques learned in Chapter 5 is that typically, the popula-tion mean ( ) and standard deviation (˙) are not known. The*conclusion*that*a*change*isjustified*isidentified*with* H a,*and*it*would*take*conclusive*evidence*to*justify rejecting*H 0 and*switching*to*the*new*coating. 31 0 obj endobj Try to solve a question by yourself first before you look at the solution. (Testing a hypothesis) The problem of how to nd a critical value for a desired level of signi cance of the hypothesis test will be studied later. endobj Use the test statistic to determine the p-value. 15 0 obj (General concepts) Two-tailed hypothesis test example Problem: A premium golf ball production line must produce all of its balls to 1.615 ounces in order to get the top rating (and therefore the top dollar). A well worked up hypothesis is half the answer to the research question. The test statistic t is a standardized difference between the means of the two samples. Whether you use a 1-tailed or 2-tailed test depends on the nature of the problem. (Hint for exam: no student project should ever violate this nor have to assume it. Hypothesis Testing Problems | Superprof A hypothesis based problem-solving approach is looking at the bigger picture and taking a broad view of the situation, making xڵSMOA��q�0��}��нU= H $�D��ڻ�M�� b��g�� XW��HI� \d�. In this method, we test some hypothesis by determining the likelihood that a sample statistic could have been selected, if the hypothesis regarding the population parameter were true. endobj << /S /GoTo /D (Outline0.5) >> 32 0 obj (iii) = 0:05. Hypothesis Testing Solved Problems Pdf - localexam.com Participants are randomly selected 3. Scientificresearch*often*involvestrying*to*decide*whether*a* 19 0 obj endobj << /S /GoTo /D [37 0 R /Fit ] >> We indicate that the average study time is either 20 hours per week, or it is not. Samples are drawn hourly and checked. << /S /GoTo /D (Outline0.1) >> 36 0 obj 16 0 obj The test statistics is t x̄ − s n 6.3 −7 2.1 35 ≈−1.97 Since the test statistic is not in the critical region, the conclusion is: Failure to reject the null hypothesis. endobj Hypothesis Testing One type of statistical inference, estimation, was discussed in Chapter 5. (iv)The degrees of freedom: k 1 = 5 1 = 4. >> 35 0 obj Hypothesis Testing The idea of hypothesis testing is: Ask a question with two possible answers Design a test, or calculation of data Base the decision (answer) on the test Example: In 2010, 24% of children were dressed as Justin Bieber for Halloween. 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(Tests concerning sample mean $variance known$) endobj 2. Framework of hypothesis testing Two ways to operate: computing a p-value or through a con dence region Examples for normal distribution or proportions One-sided and two sided tests Link between hypothesis testing and con dence interval Reminder: the lecture notes contain more details and more examples; they are available on my website. << /S /GoTo /D (Outline0.7) >> If you repeat the experiment then no one would take the results seriously. Hence the decision test is to reject the null hypothesis if the test statistic is less than -2.441. endobj Assumppyp gtions of Hypothesis Testing 1. 9.2 Null and Alternate Hypotheses2 The actual test begins by considering two hypotheses. Region of rejection. Hypothesis testing or significance testing is a method for testing a claim or hypothesis about a parameter in a population, using data measured in a sample. As with any other test of significance, after the test statistic has been computed, it must be determined whether this test statistic is far enough from zero to reject the null hypothesis. Tests of Hypotheses Using Statistics Adam Massey⁄and Steven J. Millery Mathematics Department Brown University Providence, RI 02912 Abstract We present the various methods of hypothesis testing that one typically encounters in a mathematical statistics course. CH8: Hypothesis Testing Santorico - Page 290 Hypothesis Test Procedure (Traditional Method) Step 1 State the hypotheses and identify the claim. endobj 9-2 Steps in Hypothesis Testing The alternative hypothesis , symbolized by H1, is a statistical hypothesis that states a specific difference between a parameter and a specific value or states that there is a difference between two parameters. (Approximation of the binomial using the normal distribution) The 11 0 obj A hypothesis is an educated guess that analyze the things around you and it […] 18_2_sample_t_test.pdf Michael Hallstone, Ph.D. hallston@hawaii.edu Lecture 18: Two-Sample Hypothesis Test of Means Some Common Sense Assumptions for Two Sample Hypothesis Tests 1. Types of errors Because we are making a decision based on a nite sample, there is a possibility that we will make mistakes. 20 0 obj 3 0 obj The possible outcomes are: H How to Solve Hypothesis Testing Problems One common type of problem you will find in Basic Statistics homework is the type of problem that involves using sample data to test a hypothesis . Determine the null hypothesis and the alternative hypothesis. endobj yDegrees of Freedom: The number of scores that are free to vary when estimating a population parameter from a sample df = N – 1 (for a Single-Sample t Test) The focus will be on conditions for using each test, the hypothesis Step 5 Summarize the results. 'F�� L��CGG,4��2�Km�Ӌwc��)�8z�7�� pF�#Pa�%��}��4��S�t%��Y�W ��G+_ Ch��0�� (v)The test statistic can be calculated using a table: See the Table of Contents topic "Solution Sheets". << /S /GoTo /D (Outline0.2) >> 3. The result is statistically significant if the p-value is less than or equal to the level of significance. Problems with the Hypothesis Testing Approach Over the past several decades (e.g., since Berkson 1938) people have questioned the use of hypothesis testing in the sciences. Use this statistic to test the problem: 27 0 obj 23 0 obj %�� We do not specify whether we believe the true mean to be higher or lower than the hypothesized mean. The t-test is any statistical hypothesis test in which the test statistic follows a Student’s t-distribution under the null hypothesis. Read PDF Hypothesis Testing Problems And Solutions 90% confidence and the example above, with a p-value of 0.06, would reject . An independent testing agency was hired prior to the November 2010 election to study whether or not the work output is different for construction workers employed by the state and receiving prevailing wages versus construction workers in the private sector who are paid rates We will solve the following hypothesis tests for a one-population problem using the template to be designed. endobj 23.1 How Hypothesis Tests Are Reported in the News 1. P-value < 0.05. Unit 7 – Hypothesis Testing Practice Problems SOLUTIONS . Hypothesis Testing •The intent of hypothesis testing is formally examine two opposing conjectures (hypotheses), H 0 and H A •These two hypotheses are mutually exclusive and exhaustive so that one is true to the exclusion of the other •We accumulate evidence - collect and analyze sample information - for the purpose of determining which of 9-2 Steps in Hypothesis Testing A Statistical hypothesis is a conjecture about a population parameter. << /S /GoTo /D (Outline0.4) >> The null hypothesis , symbolized by H0, is a statistical hypothesis that states that there is no difference between a parameter and a specific value or that there is no difference between two parameters. %PDF-1.4 Step 2 Find the critical value(s) from the appropriate table. (p-values) Hypothesis Tests: SingleSingle--Sample Sample tTests yHypothesis test in which we compare data from one sample to a population for which we know the mean but not the standard deviation. If the production line gets out of sync with a statistical significance of more than 1%, it must be shut down and repaired. Computer use averages 3.2 hours per week, or it does not. Question 1 In the population, the average IQ is 100 with a standard deviation of 15. 8 0 obj The test variable used is appropriate for a mean (interval/ratio level). We want to test whether or not this proportion increased in 2011. (ii)The alternative hypothesis, H a: the null hypothesis is false. Journal of Academia UiTM Negeri Sembilan 4 (2016) 12-20 12 SOLVING THE STATISTICAL TEST SELECTION PROBLEM IN HYPOTHESIS TESTING Kien-Kheng, Foo1, Nuralina Azlan2, Noraini Idris3 and Siti Noor Dina Ahmad4 1 Institute of Graduate Studies, University of Malaya, Jalan Universiti,50603 Kuala Lumpur, Wilayah Persekutuan Kuala Lumpur stream It can be used to determine if two sets of data are significantly different from each other, and is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known. PROBLEM SOLVING AND GAME-BASED LEARNING: EFFECTS OF MIDDLE GRADE STUDENTS’ HYPOTHESIS TESTING STRATEGIES ON LEARNING OUTCOMES* HILLER A. SPIRES JONATHAN P. ROWE BRADFORD W. MOTT JAMES C. LESTER North Carolina State University ABSTRACT Targeted as a highly desired skill for contemporary work and life, problem endobj Hypotheses*and*Test*Procedures An*appropriate*problem*formulation*would*involve*testing* H 0: µ=1000* against*H a: µ>1000 . (One- and two-tailed tests) << /S /GoTo /D (Outline0.3) >> The other type ,hypothesis testing ,is discussed in this chapter. The distribution of the population is approximately normal RobustRobust: : These hyp. endobj Here is a list hypothesis testing exercises and solutions. H0: µ = 100 HA: µ <> 100 I. When there pdf hypothesis estimation testing products that exist, and continue to be drastically limited. 39 0 obj << For example, you could conduct a test to find either a drug is effective or not for treating headaches. The examples above are all two-tailed hypothesis tests. Text Book : Basic Concepts and Methodology for the Health Sciences 3 Reject. 28 0 obj 24 0 obj The criticisms apply to bothexperimental data (control and treatment(s), random assignment of experimental units, replication, and some “design") and endobj endobj << /pgfprgb [/Pattern /DeviceRGB] >> (i)The null hypothesis H 0:the population frequencies are equal to the expected frequencies (to be calculated below). endobj /Filter /FlateDecode H. An alternative hypothesis that specified that the parameter can lie on either side of the value specified by H0 is called a two-sided (or two-tailed) test, e.g. Plan for these notes I Describing a random variable I Expected value and variance I Probability density function I Normal distribution I Reading the table of the standard normal I Hypothesis testing on the mean I The basic intuition I Level of signi cance, p-value and power of a test I An example Michele Pi er (LSE)Hypothesis Testing for BeginnersAugust, 2011 3 / 53 Hypothesis testing is an important activity of empirical research and evidence-based medicine. (Tests concerning sample mean $variance unknown$) Usually we use a 2-tailed test. 0.01 in one tail). Test Statistic n SE H SE x x x V P P { and where population mean assuming is true z 0 0 0 stat This is an example of a one-sample test of a mean when σ is known. A hypothesis is a statement about a population parameter. 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