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Unformatted text preview: Histogram for Quiz 1 Scores Histogram for Midterm Exam Scores HYPOTHESIS TESTING: ONE SAMPLE Z AND T TESTS There are several types of hypotheses that we might test (see page 257): 1. A statement about a single parameter H : = 0 The population mean is 0. The Steps of Hypothesis Testing Examples of types of tests: 7 Hypothesis setups for testing a mean If the sample size is small and is not known, then the tstatistic is used instead of Z. How do I know what test to use? Use Zstatistic if: Use tstatistic if: If the population standard deviation (29 is known or the sample is more than 30. If the population standard deviation ( 29 is unknown and the sample is less than 30. Comparison of Zstatistic and tstatistic formulas Zstatistic Tstatistic Use the tstatistic for testing a sample mean against a population mean if is unknown and n<30. When using the tstatistic, you need to find the critical value that corresponds to n1 degrees of freedom. Tdistribution is the same as normal distribution when sample size is infinite Graph from http://cnx.org/content/m13495/latest/ Distributions of the tstatistic symmetrical and bellshaped but are flatter and more spread out (greater variability). The critical value for the tstatistic uses the t Distribution Table. 1. Decide whether youre doing a one or twotailed test. (directional vs. nondirectional) 2. Select your alpha level. 3. Find the row that corresponds to n1 degrees of freedom. Table C: Percentile points of t Distribution (p.621) Directional Nondirectional Example: 95% confidence, twotailed test, n=14 Critical value is 2.160 What are degrees of freedom? The number in a sample that are free to vary. The sample mean places a restriction on the value of one score in the sample. Therefore, there are n1 values that are free to vary. We have n1 degrees of freedom with the t statistic. Pair and Share In a singlesample ttest, what are the respective critical values for: A. =.05, n=10, twotailed test B. =.01, n=30, onetailed test C. =.05, n=28, onetailed test D. =.01, n=61, twotailed test 2.262 2.457 1.684 2.617 Review Questions 1. As the value for df gets smaller, the t distribution resembles a normal distribution more and more. (true or false?) 1. As the value for df gets larger, s provides a better estimate of . (true or false?) 3. For df = 10, what t values are associated with: a. The top 1% of the t distribution b. The bottom 5% of the t distribution c. A twotailed distribution for 99% confidence. The average writing score on a test in the population is 368. A random sample of 25 students took the test with a sample mean of 372.5 with a sample standard deviation of 15. Do the students have a different mean than the population? Test at the 0.05 level....
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