Exam 13: Asking and Answering Questions About the Difference Between Two Means

After an outbreak of a drug-resistant strain of bacteria (Enterococci faecium), hospitalofficials became concerned that their alcohol-based handrub (ABHR) hand hygieneprogram was not sufficient to prevent spreading this bacteria. The officials solicited20 volunteers to assess the effectiveness of ABHR. The volunteers' hands werecontaminated with E. faecium. After gathering baseline data on the amount ofbacteria present they performed the recommended hand hygiene according to theWorld Health Organization protocol. The amount of bacteria present was thenassessed again. Summary measures and boxplots of the baseline sample, the post-ABHR sample, and the reduction in the amount of bacteria ( log10 (bacteria / mL) ) arepresented below. Do these data provide sufficient evidence that the ABHR iseffective against the E. faecium?

The Amazon River basin includes the largest remaining connected area of tropicalforest in the world, and ecologists regularly monitor its health. One aspect of itshealth is the density of different indigenous species. The Amazon basin includes bothareas that are periodically flooded, and areas that are not periodically flooded. If thedensities of species differ in the flooded and unflooded regions, researchers will wantto take stratified samples in their studies. Stratified sampling would be moreexpensive, since boats must be rented to get to any randomly selected flooded sites.The data below are measures of density (individuals per square kilometer) of primatesin random samples of flooded and unflooded areas in the Amazon basin. a) Do these data provide convincing evidence of a difference in the primate densityin flooded and unflooded forests in Amazonia? Provide appropriate statisticaljustification for your conclusion.b) Based on your results in part (a), would you recommend using a stratified sample? Justify your recommendation with a statistical argument.

"Tail-chasing" by dogs is an anxiety disorder characterized by circling behavior withthe dog's attention directed toward its tail. There may be many reasons for tail-chasing behaviors. To investigate the potential for biochemical causes, a study wasperformed at a small animal clinic at a university. Blood samples were taken fromrandom sample of 15 dogs brought to the clinic by owners worried about the tail-chasing behaviors of their dogs. A control group consisting of a random sample of 15dogs brought to the clinic for other reasons contributed blood samples with theowner's permission. The mean lipoprotein density for the tail-chasing group was 12mg/dl, and the standard deviation was 2.24 mg/dl. The corresponding statistics forthe control group were 13 mg/dl and 1.73 mg/dl. There was no indication ofskewness in either sample distribution.a) Is there sufficient evidence to conclude that there is a difference in meanlipoprotein density in these two samples? Provide statistical justification for yourresponse.b) Irrespective of your response in part (a), consider the design of this study. Woulda statistically significant difference in mean lipoprotein density be sufficient tomake a case that lipoprotein density is the cause of tail-chasing behavior in dogs? Why or why not?

In many animal species the males and females differ slightly in structure, coloring,and/or size. The hominid species Australopithecus is thought to have lived about 3.2million years ago. ("Lucy," the famous near-complete skeleton discovered in 1974, isan Australopithecus.) Forensic anthropologists use partial skeletal remains toestimate the mass of an individual. The data below are estimates of masses frompartial skeletal remains of this species found in sub-Saharan Africa. Appropriategraphical displays of the data indicate that it is reasonable to assume that thepopulation distributions of mass are approximately normal for both males andfemales. You may also assume that these samples are representative of the respectivepopulations. Do these data provide convincing evidence that the mean estimated masses differ forAustralopithecus males and females? Provide appropriate statistical justification foryour conclusion.

When an alternative hypothesis is 0he P-value is found bydoubling the appropriate area under the t curve.

When wildlife biologists study small animals, the animals are trapped and thenanesthetized to prevent discomfort to the animal. A study of the effect of theanesthetic, Isoflurane, on Allegheny woodrats (Neotoma magister) resulted in theheartbeat data presented below. The biologists were interested in comparing theeffects of Isoflurane in two different seasons, winter and summer. An initial analysis of the data revealed that it was reasonable to assume thedistributions of heartbeats for both seasons are approximately normal. It was alsojudged to be reasonable to regard these samples as representative of the Alleghenywoodrat population. a) Test the hypothesis of no difference between woodrat mean heartbeat rates forwinter and summer. b) Do the data indicate that the mean heartbeat rates differ? Provide an appropriatestatistical justification using your response in part (a).