In Canada, do young males (Y) weigh more than older males (O) onaverage? To investigate this question, weights of eighteen malesrandomly selected from each group were recorded. Summary statisticsare given in the following table. Assume weight of each groupfollows a normal distribution. (If you think the samples areindependent, then assume equal variances.)
Summary statistics | Young (Y) | Old (O) | Pooled | Difference |
Average (kg) | 82.10 | 75.40 | | 6.70 |
Standard Deviation (kg) | 16.80 | 14.30 | 15.60 | 5.20 |
What will be the respective degrees of freedom and theP-value range for testing if young Canadian males weighmore than older males on average?
Twelve inspectors, each using two different kinds of calipers,measured the diameter of a ball bearing. Summary statistics aregiven in the following table. Assume both samples come from normaldistributions. (If you think the samples are independent, thenassume equal variances.)
Summary statistics | Caliper 1 | Caliper 2 | Pooled | Difference |
Average (mm) | 0.267 | 0.265 | | 0.002 |
Standard Deviation (mm) | 0.0024 | 0.0022 | 0.0023 | 0.0021 |
What is the margin of error for a 95% confidence interval forthe difference in mean diameter measurements for the two kinds ofcalipers?
Twelve inspectors, each using two different kinds of calipers,measured the diameter of a ball bearing. Summary statistics aregiven in the following table. Assume both samples come from normaldistributions. (If you think the samples are independent, thenassume equal variances.)
Summary statistics | Caliper 1 | Caliper 2 | Pooled | Difference |
Average (mm) | 0.267 | 0.263 | | 0.004 |
Standard Deviation (mm) | 0.0056 | 0.0079 | 0.0068 | 0.0041 |
Is there a difference in mean diameter measurements for the twokinds of calipers? In performing this hypothesis test, what is theP-value range based on the t-table andthe conclusion at the 1% significance level?
