1. In many animal species the males and females differ slightlyin structure, coloring, and/or size. The hominid speciesAustralopithecus is thought to have lived about 3.2 million yearsago. (“Lucy,†the famous near complete skeleton discovered in 1974,is an Australopithecus .) Forensic anthropologists use partialskeletal remains to estimate the mass of an individual. The databelow are estimates of masses from partial skeletal remains of thisspecies found in sub-Saharan Africa. Appropriate graphical displaysof the data indicate that it is reasonable to assume that thepopulation distributions of mass are approximately normal for bothmales and females. You may also assume that these samples arerepresentative of the respective populations. Estimates of mass(kg)
Males 51.0, 45.4, 45.6, 50.1, 41.3, 42.6, 40.2, 48.2, 38.4,45.4, 40.7, 37.9, 41.3, 31.5
Females 27.1, 33.5, 28.0, 30.3, 32.7, 32.5, 34.2, 30.5, 27.5,23.3,35.7
Do these data provide convincing evidence that the meanestimated masses differ for Australopithecus males and females?Provide appropriate statistical justification for yourconclusion.
2. In an introductory marketing class students were presentedwith 6 items they could bid on in an auction. They were asked tobid privately and also estimate the “typical†bid for each item bytheir classmates. The items were randomly selected from a largelist of items that students might purchase. An initial analysis ofthe data established the plausibility that the distribution ofdifferences (estimated – actual) is approximately normal.
Construct a 95% confidence interval for the mean differencebetween the actual bid and the estimated “typical†bid for thepopulation of items.
| GOOD | ACTUAL | ESTIMATE | DIFFERENCE |
| Teddy bear | 1.00 | 4.90 | 3.90 |
| Music CD | 1.25 | 4.53 | 3.28 |
| sachet | 2.70 | 5.44 | 2.74 |
| wood puzzle | 3.00 | 5.17 | 2.17 |
| smoked salmon | 3.00 | 6.67 | 3.67 |
| jelly beans | 4.00 | 7.30 | 3.30 |
