Session__8a

# Session__8a - Histogram for Quiz 1 Scores Histogram for...

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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 : μ = 0 The population mean is 0. The Steps of Hypothesis Testing Examples of types of tests: 7 Hypothesis set-ups for testing a mean If the sample size is small and σ is not known, then the t-statistic is used instead of Z. How do I know what test to use? Use Z-statistic if: Use t-statistic if: If the population standard deviation (σ29 is known or the sample is more than 30. If the population standard deviation ( σ29 is unknown and the sample is less than 30. Comparison of Z-statistic and t-statistic formulas Z-statistic T-statistic Use the t-statistic for testing a sample mean against a population mean if σ is unknown and n<30. When using the t-statistic, you need to find the critical value that corresponds to n-1 degrees of freedom. T-distribution is the same as normal distribution when sample size is infinite Graph from http://cnx.org/content/m13495/latest/ Distributions of the t-statistic symmetrical and bell-shaped but are flatter and more spread out (greater variability). The critical value for the t-statistic uses the t- Distribution Table. 1. Decide whether you’re doing a one or two-tailed test. (directional vs. non-directional) 2. Select your alpha level. 3. Find the row that corresponds to n-1 degrees of freedom. Table C: Percentile points of t- Distribution (p.621) Directional Non-directional Example: 95% confidence, two-tailed 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 n-1 values that are free to vary. We have n-1 degrees of freedom with the t statistic. Pair and Share In a single-sample t-test, what are the respective critical values for: A.α =.05, n=10, two-tailed test B. α =.01, n=30, one-tailed test C. α =.05, n=28, one-tailed test D. α =.01, n=61, two-tailed 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 σ. (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 two-tailed 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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Session__8a - Histogram for Quiz 1 Scores Histogram for...

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