Defective Pacemakers Among 8834 cases of heart pacemaker malfunctions, 504 were found to be caused by firmware, which is software programmed into the device (based on data from “Pacemaker and ICD Generator Malfunctions,” by Maisel et al., Journal of the American Medical Association, Vol. 295, No. 16). If the firmware is tested in three different pacemakers randomly selected from this batch of 8834 and the entire batch is accepted if there are no failures, what is the probability that the firmware in the entire batch will be accepted? Is this procedure likely to result in the entire batch being accepted?

One hundred patients with moderate‑to‑severe knee osteoarthritis who were eligible for a total knee replacement were enrolled in a randomized controlled study. Fifty patients were assigned to receive a total knee replacement with a 12-week12-week follow‑up of nonsurgical treatment consisting of exercise, education, dietary advice, use of insoles, and pain medication. The other 5050 patients received only the 1212 weeks of nonsurgical treatment. One purpose of the randomization is for the two groups to have similar levels of knee osteoarthritis before undergoing the treatments. After the random assignment, we can compare the two treatment groups to see how well the randomization worked. The Kellgren‑Lawrence score, which can take the values 0,0, 1,1, 2,2, 3,3, or 4,4, is based on a standard X‑ray and assesses the severity of knee osteoarthritis, with 00 indicating no osteoarthritis and 44 indicating the most severe symptoms. If the randomization worked, then both treatment groups should…

In the past 10 years, the prevalence of peanut allergies has doubled in Western countries. Is consumption or avoidance of peanuts in infants related to the development of peanut allergies in infants at risk? Subjects included infants between four and 11 months with severe eczema, egg allergy, or both but who did not display a preexisting sensitivity to peanuts based on a skin-prick test. The infants were randomly assigned to either a treatment that avoided consuming peanut protein or a treatment in which at least 6 grams of peanut protein were consumed per week. The response was the presence or absence of peanut allergy at 60 months of age. In the avoidance group containing 263 infants, 36 had developed a peanut allergy at 60 months of age, while in the consumption group containing 266 infants, five had developed a peanut allergy. George Du Toit et al., "Randomized trial of peanut consumption in infants at risk for peanut allergy," New England Journal of Medicine, 372 (2015), pp.…

In a one-way analysis of variance with three treatments, each with five measurements, in which a completely randomized design is used, what is the degrees of freedom for treatments?  a. 5 b. 2 c. 4 d. 8

Researchers studying the link between prenatal vitamin use and autism surveyed the mothers of a random sample of children aged 24 - 60 months with autism and surveyed another separate random sample for children with typical development. Table summarizing the number of mothers in each group who did and did not use prenatal vitamins during the three months before pregnancy (data from Schmidt, 2011) Autism Typical Development Total No vitamin 111 70 181 Vitamin 143 159 302 Total 254 229 483 Complete the hypothesis test for independence between the two variables, use of prenatal vitamins during the three months before pregnancy and autism in Rguroo. What is the value of the test statistic for this test? (Use the Large Sample Z method and please round to two decimal places)

To test for any significant difference in the number of hours between breakdowns for four machines, the following data were obtained. Machine Machine 2 1 6.4 7.9 5.3 7.6 8.4 7.6 8.6 7.3 Ha: M₁ M₂ # 9.4 10.2 9.3 9.8 Ho: M₁ = M₂ = M3 = μ4 M3 ‡ M4 # Ho: M₁ M₂ # M3 ‡ M4 На: M1 = M2 = M3=Ма Machine 3 10.8 Ho: M₁ = M₂ = M3 = M4 Ha: 10.1 9.5 10.2 8.9 8.7 Machine 4 9.7 12.8 12.1 (a) At the α = 0.05 level of significance, what is the difference, if any, in the population mean times among the four machines? State the null and alternative hypotheses. 10.7 11.1 11.4 Ho: At least two of the population means are equal. H₂: At least two of the population means are different. Not all the population means are equal. Ho: Not all the population means are equal. На: M1 = M2 = M3 = M4

A study was made of 413 children who were hospitalized as a result of motor vehicle crashes. Among 290 children who were not using seat belts, 60 were injured severely. Among 123 children using seat belts, 16 were injured severely (based on data from "Morbidity Among Pediatric Motor Vehicle Crash Victims: The Effectiveness of Seat Belts," by Osberg and Di Scala, American Journal of Public Health, Vol. 82, No. 3). For this problem we want to know, is there sufficient sample evidence to conclude, at the 0.05 significance level, that the proportion of severe injuries is higher for children not wearing seat belts? Let pi be the proportion of severe injuries among all children not wearing seatbelts and who were involved in crashes. Let p2 be the proportion of severe injuries among all children wearing seatbelts and who were involved in crashes. Which is the proper expression of Ho? Pi = P2 O Pi P2 Which is the proper expression of H1? O pi P2 Calculate p1 to 4 decimal places: Calculate p,…