1. 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.

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

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

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

5. Time (minutes) Sex=F Sex=M 55.87 69.20 13.527 13.790 3.4927 3.5606 15
Mean
55.87
69.20
Std Dev
13.527
13.790
Std Err Mean
3.4927
3.5606 N 15

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

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

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

9. Females
Time (min)

10. Males
Time (min)

11. 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.

12. Confidence Interval for

15. 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.

16. Table T df 1 2 3 4 28
2.048
Confidence Levels 80% % % % %

17. Confidence Interval for

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

19. 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?

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

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

22. Females
Time (min)

23. Males
Time (min)

24. 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.

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

26. Time (minutes) Sex=F Sex=M 55.87 69.20 13.527 13.790 3.4927 3.5606 15
Mean
55.87
69.20
Std Dev
13.527
13.790
Std Err Mean
3.4927
3.5606 N 15

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

29. Table T Two tail probability 0.20 0.10 0.05 0.02 P-value 0.01 df 1 2 34 28

30. 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.

31. 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.

32. 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.

33. Alternatives

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

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