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? ?

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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…

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.

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.

a pathological video game user(PVGU) is à video game user averages 31 or more hours a week of of gameplay.

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?

Researchers investigate how the presence of cell phones influence the quality of human interaction.  Subjects are randomly selected from a population and divided into an experimental group that is asked to leave their phones in the front of the room and a control group that are not asked to leave their cell phones at the front of the room.  Subjects are left alone for 10 minutes and then asked to take a survey designed to measure quality of interactions they had with others in the experiment.  What statistical test is appropriate?

Popular Diets. In the article “Comparison of the Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Risk Reduction” (Journal of the American Medical Association, Vol. 293, No. 1, pp. 43–53), M. Dansinger et al. conducted a randomized trial to assess the effectiveness of four popular diets for weight loss. Overweight adults with average body mass index of 35 and ages 22–72 years participated in the randomized trial for 1 year. The weight losses, in kilograms, based on the results of the experiment are given on the WeissStats site. Negative losses are gains. WW = Weight Watchers. a. Obtain individual normal probability plots and the standard deviations of the samples. b. Perform a residual analysis. c. Use your results from parts (a) and (b) to decide whether conducting a one-way ANOVA test on the data is reasonable. If so, also do parts (d) and (e). d. Use a one-way ANOVA test to decide, at the 5% significance level, whether the data provide sufficient…

Football and Brain SizeA study examines a possible relationship of football playing and concussions on hippocampus volume, in μL, in the brain. The study included three groups: controls who had never played football (Control), football players with no history of concussions (FBNoConcuss), and football players with a history of concussions (FBConcuss). The data is available in FootballBrain, and the side-by-side boxplots shown below indicate that the conditions for using the F-distribution appear to be met. b) Use technology to construct an ANOVA table. What is the F-statistic? What is the p-value? Round your answer for the F-statistic to two decimal places, and your answer for the p-value to three decimal places.F-statistic = ?p-value = ?   Group Hipp LeftHipp Years Cogniton Control 6175 2945 0   Control 6220 3075 0   Control 6360 3125 0   Control 6465 3160 0   Control 6540 3205 0   Control 6780 3340 0…