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Lesson 9.3a Hypothesis Test for Means

Lesson 9.3a Hypothesis Test for Means. Formulas:. m. t =. About t-tests. Calculating a p-value For t-test statistic – tcdf(lowerbound, upperbound, df). Draw & shade a curve & calculate the p-value:. 1) right-tail test t = 1.6; n = 20 2) two-tail test t = 2.3; n = 25. P-value = .0630.

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Lesson 9.3a Hypothesis Test for Means

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  1. Lesson 9.3aHypothesis Test for Means

  2. Formulas: m t =

  3. About t-tests Calculating a p-value • For t-test statistic – tcdf(lowerbound, upperbound, df)

  4. Draw & shade a curve & calculate the p-value: 1) right-tail test t = 1.6; n = 20 2) two-tail test t = 2.3; n = 25 P-value = .0630 P-value = (.0152)2 = .0304

  5. Example : The Degree of Reading Power (DRP) is a test of the reading ability of children. Here are DRP scores for a random sample of 44 third-grade students in a suburban district: 40 26 39 14 42 18 25 54 41 43 46 27 19 47 19 26 45 51 35 34 15 44 40 38 31 48 27 46 52 25 35 35 33 29 22 14 34 41 49 28 52 47 35 33 At the a = .1, is there sufficient evidence to suggest that this district’s third graders reading ability is different than the national mean of 34?

  6. H0: m = 34 Ha: m = 34 Let m represent the actual mean reading ability of the district’s third-graders SRS? 10%? • SRS given • 44 < 10% of the district’s 3rd graders Parameter? Normal? How do you know? • Nearly Normal? Yes  CLT n=44 > 30 What are your hypothesis statements? One-sample t-test Name the test? a = .1 df = 44 – 1 = 43 Find the test statistic... t! p-value = tcdf(.6467,999,43)=.2606(2)=.5212 Use tcdf to calculate p-value.

  7. Compare your p-value to a & make decision Conclusion: Since p-value (.5212) > a (.1), I fail to reject the null hypothesis. There is not sufficient evidence to suggest that the true mean reading ability of the district’s third-graders is different than the national mean of 34. Write conclusion in context in terms of Ha.

  8. Example : The Wall Street Journal (January 27, 1994) reported that based on sales in a chain of Midwestern grocery stores, President’s Choice Chocolate Chip Cookies were selling at a mean rate of $1323 per week. Suppose a random sample of 30 weeks in 1995 in the same stores showed that the cookies were selling at the average rate of $1208 with standard deviation of $275. Does this indicate that the sales of the cookies has declined since 1994? =.05

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