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.
Inference for Do males and females at I.S.U. spend the same amount of time, on average, at the Lied Recreation Athletic Center?
Populations Inference Samples 1. Female 2. Male random random selection random selection Samples
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
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
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.
Conditions & Assumptions Randomization Condition 10% Condition Nearly Normal Condition Independent Groups Assumption How were the data collected?
Conditions & Assumptions Randomization Condition Random sample of males. Random sample of females. Independence Assumption Two separate random samples. 10% Condition
Females Time (min)
Males Time (min)
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.
Confidence Interval for
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.
Table T df 1 2 3 4 28 2.048 Confidence Levels 80% 90% 95% 98% 99%
Confidence Interval for
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.
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?
Test of Hypothesis for Step 1: Set up the null and alternative hypotheses.
Test of Hypothesis for Step 2: Check Conditions. Randomization Condition Two Independent Random Samples 10% Condition Nearly Normal Condition
Females Time (min)
Males Time (min)
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.
Test of Hypothesis for Step 3: Compute the value of the test statistic and find the P-value.
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
Test of Hypothesis for Step 3: Compute the value of the test statistic and find the P-value.
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
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.
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.
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.
Alternatives
JMP Data in two columns. Response variable: Explanatory variable: Numeric – Continuous Explanatory variable: Character – Nominal
JMP Starter Basic – Two-Sample t-Test Y, Response: Time X, Grouping: Sex