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Chapter 24

Chapter 24. Comparing Means. Inference for. Who? Students at I.S.U. What? Time (minutes). When? Fall 2000. Where? Lied Recreation Athletic Center. How? Measure time from when student arrives on 2 nd floor until she/he leaves. Why? Part of a Stat 101 data collection project. Inference for.

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Chapter 24

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  1. Chapter 24 Comparing Means

  2. Inference for • Who? Students at I.S.U. • What? Time (minutes). • When? Fall 2000. • Where? Lied Recreation Athletic Center. • How? Measure time from when student arrives on 2nd floor until she/he leaves. • Why? Part of a Stat 101 data collection project.

  3. Inference for • Do males and females at I.S.U. spend the same amount of time, on average, at the Lied Recreation Athletic Center?

  4. Populations 1. Female 2. Male Inference random selection random selection Samples

  5. Time (minutes) 1. Females 2. Males 63, 32, 86, 53, 49 52, 75, 74, 68, 93 73, 39, 56, 45, 67 77, 41, 87, 72, 53 49, 51, 65, 54, 56 84, 65, 66, 69, 62

  6. Time (minutes)

  7. Comment • This sample of I.S.U. females spends, on average, 13.33 minutes less time at the Lied Recreation Athletic Center than this sample of I.S.U. males.

  8. Conditions & Assumptions • Randomization Condition • 10% Condition • Nearly Normal Condition • Independent Groups Assumption • How were the data collected?

  9. Conditions & Assumptions • Randomization Condition • Random sample of males. • Random sample of females. • Independence Assumption • Two separate random samples. • 10% Condition

  10. Females Time (min)

  11. Males Time (min)

  12. Nearly Normal Condition • The female sample data could have come from a population with a normal model. • The male sample data could have come from a population with a normal model.

  13. Confidence Interval for

  14. Finding t* • Use Table T. • Confidence Level in last row. • df = a really nasty formula (so the value will be given to you). • df = 28 for our example.

  15. Table T df 1 2 3 4 28 2.048 Confidence Levels 80% 90% 95% 98% 99%

  16. Confidence Interval for

  17. Interpretation • We are 95% confident that I.S.U. females spend, on average, from 3.11 to 23.55 minutes less time at the Lied Recreation Athletic Center than I.S.U. males do.

  18. Inference for • Do males and females at I.S.U. spend the same amount of time, on average, at the Lied Recreation Athletic Center? • Could the difference between the population mean times be zero?

  19. Test of Hypothesis for • Step 1: Set up the null and alternative hypotheses.

  20. Test of Hypothesis for • Step 2: Check Conditions. • Randomization Condition • Two Independent Random Samples • 10% Condition • Nearly Normal Condition

  21. Females Time (min)

  22. Males Time (min)

  23. Nearly Normal Condition • The female sample data could have come from a population with a normal model. • The male sample data could have come from a population with a normal model.

  24. Test of Hypothesis for • Step 3: Compute the value of the test statistic and find the P-value.

  25. Time (minutes)

  26. Test of Hypothesis for • Step 3: Compute the value of the test statistic and find the P-value.

  27. Table T Two tail probability 0.20 0.10 0.05 0.02 P-value 0.01 df 1 2 3 4 28 1.313 1.701 2.048 2.467 2.672 2.763

  28. Test of Hypothesis for • Step 4: Use the P-value to make a decision. • Because the P-value is small (it is between 0.01 and 0.02), we should reject the null hypothesis.

  29. Test of Hypothesis for • Step 5: State a conclusion within the context of the problem. • The difference in mean times is not zero. Therefore, on average, females and males at I.S.U. spend different amounts of time at the Lied Recreation Athletic Center.

  30. Comment • This conclusion agrees with the results of the confidence interval. • Zero is not contained in the 95% confidence interval (–23.55 mins to –3.11 mins), therefore the difference in population mean times is not zero.

  31. Alternatives

  32. JMP • Data in two columns. • Response variable: • Numeric – Continuous • Explanatory variable: • Character – Nominal

  33. JMP Starter • Basic – Two-Sample t-Test • Y, Response: Time • X, Grouping: Sex

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