STAT 250 Project IV Test for association between two categorical variables

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 conducted another separate random sample for children with typical development. The table below shows the number of mothers in who did and did not use prenatal vitamins during the three months before pregnancy (periconceptional period). each group Autism Typical Development Total No Vitamin 115 75 190 Took Vitamins 145 161 306 Total 260 236 496 State and conduct the appropriate hypotheses to test for independence of use of prenatal vitamins during the three months before autism. Use significance level = 0.01. pregnancy and Но : propi — prop2 ? HA: propi - – prop2? p-value: Based on this information, we may What type of error could we have made? ?

A pathological video game user (PVGU) is a video game user that averages 31 or more hours a week of gameplay. According to the article “Pathological Video Game Use among Youths: A Two-Year Longitudinal Study” (Pediatrics, Vol. 127, No. 2, pp. 319–329) by D. Gentile et al., in 2011, about 9% of children in grades 3–8 were PVGUs. Suppose that, today, five youths in grades 3–8 are randomly selected. Let X represent the number of youths who are PVGUs. Calculate the probability that EXACTLY three youths are PVGUs

A pathological video game user (PVGU) is a video game user that averages 31 or more hours a week of gameplay. According to the article “Pathological Video Game Use among Youths: A Two-Year Longitudinal Study” (Pediatrics, Vol. 127, No. 2, pp. 319–329) by D. Gentile et al., in 2011, about 9% of children in grades 3–8 were PVGUs. Suppose that, today, five youths in grades 3–8 are randomly selected. Let X represent the number of youths who are PVGUs. n =  p =  1 – p =  Prepare the probability distribution for the random variable X. Complete the following table. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. X = x P(X=x) 0   1   2   3   4   5     ∑=1.0000∑=1.0000  Calculate the probability that EXACTLY three youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. P(X = 3) =  Calculate the probability that AT LEAST two youths are PVGUs. Round your answers to 4 decimal places e.g. 0.XXXX or .XXXX. P(X ≥ 2) =  Calculate the…

Vasectomies and Prostate Cancer. In the United States, approximately 450,000 vasectomies are performed each year. In this surgical procedure for contraception, the tube carrying sperm from the testicles is cut and tied. Several studies have been conducted to analyze the relationship between vasectomies and prostate cancer. The results of one such study by E. Giovannucci et al. appeared in the paper “A Retrospective Cohort Study of Vasectomy and Prostate Cancer in U.S. Men” (Journal of the American Medical Association, Vol. 269(7), pp. 878–882). Of 21,300 men who had not had a vasectomy, 69 were found to have prostate cancer; of 22,000 men who had had a vasectomy, 113 were found to have prostate cancer. a. At the 1% significance level, do the data provide sufficient evidence to conclude that men who have had a vasectomy are at greater risk of having prostate cancer? Consider men who had had a vasectomy Population 2. b. Is this study a designed experiment or an observational study?…

30. Northwest Atlantic Cod. Researchers M. Kroll et al. studied the influence of paternity on rates of mortality and development in eggs and larvae of Northwest Atlantic cod in the article, “Paternal Ef- fects on Early Life History Traits in Northwest Atlantic Cod, Gadus morhua" (Journal of Applied Ichthyology, Vol. 29, Issue 3, pp. 623– 629). A sample of adult male Northwest Atlantic cod was collected in Nova Scotia, Canada. The following table gives the lengths, in cen- timeters (cm), of the cod sampled. 47.6 65.1 54.6 48.5 58.6 67.9 48.1 62.5 52.4 55.4 57.1 55.8 a. Using Table III in Appendix A, construct a normal probability plot of the given data. b. Use part (a) to identify any outliers. c. Use part (a) to assess the normality of the variable under consid- eration.

Hepatitis B and Pancreatic Cancer. The article “Study Links Hepatitis B and Cancer of Pancreas” by D. Grady, appeared in the September 29, 2008 issue of the NewYork Times. It reported that, for the first time, a study showed that people with pancreatic cancer are more likely than those without the disease to have been infected with the hepatitis B virus. The study by M. Hassan et al., titled “Association Between Hepatitis B Virus and Pancreatic Cancer” (Journal of Clinical Oncology, Vol. 26, No. 28, pp. 4557–4562) compared 476 people who had pancreatic cancer with 879 healthy control subjects. All were tested to see whether they had ever been infected with the viruses that cause hepatitis B or hepatitis C. The results were that no connection was found to hepatitis C, but the cancer patients were twice as likely as the healthy subjects to have had hepatitis B. The researchers noted, however, that “. . . while the study showed an association, it did not prove cause and effect. More work…

Autism and Maternal Antidepressant Use A recent study41 compared 298 children with Autism Spectrum Disorder to 1507 randomly selected control children without the disorder. Of the children with autism, 20 of the mothers had used antidepressant drugs during the year before pregnancy or the first trimester of pregnancy. Of the control children, 50 of the mothers had used the drugs. (a)   Is there a significant association between prenatal exposure to antidepressant medicine and the risk of autism? Test whether the results are significant at the 5% level. (b)   Can we conclude that prenatal exposure to antidepressant medicine increases the risk of autism in the child? Why or why not? (c)   The article describing the study contains the sentence “No increase in risk was found for mothers with a history of mental health treatment in the absence of prenatal exposure to selective serotonin reuptake inhibitors [antidepressants].” Why did the researchers conduct this extra analysis?

Kava is a beverage or extract that is made from Piper methysticum, a plant native to the western Pacific islands. Suppose that, in a randomized comparative experiment to determine if taking kava daily can reduce insomnia, a group of participants with insomnia were randomly assigned to take kava (treatment group) or a placebo (control group). After six weeks, the participants were interviewed to see if they experienced a decrease in insomnia. The table shows the results from the sample. The counts are the number of people in each group who experienced a decrease in insomnia. Group Description Population proportion Sample size Sample count Sample proportion 1 Treatment (kava) P1 n₁ = 402 x1 = 213 P₁ = 0.5299 2 Control (placebo) P2 n₂ = 521 x₂ = 121 P2 = 0.2322 Compute the standard error estimate, SE, of the difference in the sample proportions. Give your answer to at least four decimal places. 0.0438 SE = Incorrect Determine the value of the two-sample z-statistic for the difference in…

Worker Fatigue. A study by M. Chen et al. titled “Heat Stress Evaluation andWorker Fatigue in a Steel Plant” (American Industrial Hygiene Association, Vol. 64, pp. 352–359) assessed fatigue in steelplant workers due to heat stress. Among other things, the researchers monitored the heart rates of a random sample of 29 casting workers. A hypothesis test is to be conducted to decide whether the mean postwork heart rate of casting workers exceeds the normal resting heart rate of 72 beats per minute (bpm). a. determine the null hypothesis. b. determine the alternative hypothesis. c. classify the hypothesis test as two tailed, left tailed, or right tailed.

"Does ginkgo improve memory?" The law allows marketers of herbs and other natural substances to make health claims that are not supported by evidence. Brands of ginkgo extract claim to "improve memory and concentration." A randomized experiment found some statistically significant evidence for such effects. The subjects were 250 healthy volunteers over 65 years old. They were randomly assigned to take ginkgo or a placebo pill (a dummy pill that looks and tastes the same). All the subjects took a battery of tests for learning and memory before treatment started and again after six weeks. a). The article said the study was double-blind. What does this mean in the context of this study? Be very specific on who's being blinded and explain why they should be blinded. b). You suspect physical fitness and mental fitness go hand-in-hand. Create a flow chart to describe a design for an experiment to include the confounding variable physical fitness. Be very specific in your design. Include all…

Is Seat Belt Use Independent of Cigarette Smoking?A study of seat belt users and nonusers yielded the randomly selected sample data summarized in the given table (based on data from “What Kinds of People Do Not Use Seat Belts?” by Helsing and Comstock,American Journal of Public Health,Vol. 67, No. 11). Test the claim that the amount of smoking is independent of seat belt use. A plausible theory is that people who smoke more are less concerned about their health and safety and are therefore less inclined to wear seat belts. Is this theory supported by the sample data?