ADM 2304 Lecture Notes - Lecture 13: Pooled Variance, Type I And Type Ii Errors, Minitab

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lilachippopotamus32

13 May 2017

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> thus, there is a 26% chance that we are wrong on at least one of the intervals. > the only way to x this is to choose a higher alpha so that the family con dence level is 95% > the bonferroni method ensures that the overall probability of a type i error in all the tests is ! > if we want to have an overall family con dence level of 100(1 - ! )% then we need each con dence interval to have a 100(1 - !/6)% con dence level. > similarly, rather than nd a critical t-value that cuts off a probability of !/2 in the right-hand tail, we need to nd a critical t-value that cuts off a probability of !/12 in the right-hand tail. We can give simultaneous c. i. for each pair of means:

Related Questions

2. (12 marks) In a study of 85 individuals, food questionnaires were used to measure the change in polyunsaturated fatty acids (PUFA) intake from the beginning to the end of the study. In addition researchers measured a genetic marker in the TNF-αgene; for this analysis, we will take the two values of this TNF-αvariable to be A- or A+. The researchers also collected information on gender, age and BMI. The primary question of interest is whether TNF-αmodiﬁes the eﬀect of PUFA on HDL.

(a) (1 mark) Let TNFa be a variable with value 1 for A+ and 0 for A- TNF-αstatus and

let gender be 1 for males and 0 for females. State a linear model for mean change in HDL that includes the predictors PUFA, TNFa, PUFA×TNFa interaction, and eﬀects for gender, age and BMI.

(b) (1 mark) A summary of the ﬁtted model is:

Estimate Std. Error t value Pr(>|t|)

(Intercept) 0.037531 0.196980 0.191 0.8494

pufa 0.019143 0.009245 2.071 0.0417

TNFa 0.074433 0.034128 2.181 0.0322

gender -0.008988 0.031793 -0.283 0.7781

age -0.003895 0.002156 -1.806 0.0747

bmi 0.006777 0.004332 1.565 0.1217

pufa:TNFa -0.024575 0.017844 -1.377 0.1724

Write a short sentence to describe why we would even consider removing gender from the model (i.e., why we would not just be happy with the above model from

the outset).

(c) (2 marks) Below is a summary of the model ﬁt without gender. Using our 10% rule-of-thumb, is there any evidence that gender confounds the PUFA×TNFa eﬀect?

If so why, if not why not?

Estimate Std. Error t value Pr(>|t|)

(Intercept) 0.024467 0.190364 0.129 0.8981

pufa 0.018841 0.009130 2.064 0.0423

TNFa 0.074850 0.033897 2.208 0.0301

age -0.003783 0.002107 -1.795 0.0765

bmi 0.006835 0.004301 1.589 0.1161

pufa:TNFa -0.024496 0.017737 -1.381 0.1712

(d) (2 marks) The researchers decided to use the model with PUFA, TNFa, PUFA×TNFa, age and BMI for inference of PUFA×TNFa interaction. What are the degrees of

freedom for the t-distribution whose critical value we need to construct conﬁdence intervals for the interaction? What upper tail probability should you use for a 95%

conﬁdence interval?

(e) (1 mark) The appropriate critical value is 1.96. Construct a 95% conﬁdence interval for the interaction.

(f) (2 marks) State the null hypothesis and a two-sided alternative hypothesis for testing whether TNFa modiﬁes the eﬀect of PUFA on HDL.

(g) (1 mark) From the computer output, what is the p-value for this test?

(h) (2 marks) For ﬁxed age and BMI, what is the estimated eﬀect of a one-unit change in PUFA for a subject who is A- at TNF-α? For ﬁxed age and BMI, what is the estimated eﬀect of a one-unit change in PUFA for a subject who is A+ at TNF-α.

crimsonyellowjacket200

I would like to prove the last part (d).

Thank you

proof read please

Society is changing constantly and families has different point of view of how to live their life or raise their kids. I think what we know so far as a family will change in the near future. Furthermore for my own personal experience I have seen great thing from the changes that have come over the past years to now and it was acceptable by the society however, People and society in general like good changes. My grandma at age of 13 yrs. old had kids and spouse and they used to stay home raising their kids and taking care the house, while spouse were working to bring food to their tablet and older kids in the household used to work to support their parent home too Versus now in 2016 that family are disintegrating, kids are isolating themselves from their family due to the technology and you see more divorce. I could imagine how family will be 100 year from now. I have seen that woman wants to be more independently and having kids is not their priority anymore because I feel that it wonât be no family 50 to 100 year from now. It will be a law that marriage couple are going to have 1 year marriage contract. I can say that many values come from our parents and most are very worthwhile and I pass those values to my kids and I would like to retain them, but Family values are different from culture to culture and tradition and there will be change by the time, based on these I could say that it wonât be moral and immoral activities 50 year from now. We are goings lose moral value and ethic and I will see population decrease causing higher dead and less birth because government will soon controlling family life by limit how many kids a marriage couple could have. Since technology offer a good and effectively way to keep in touch with family around the world, but I also think technology will also affect family in the household. However, technology is taking control when the one on one communication is falling apart. The social media preventing family from communicating and less interaction with family and the society wonât have too much talking. I probably happy to say that the only positive thing that I will see 50 to 100 year from now will be major diseases like Heart attack , diabetes and cancer will largely preventing by the time with new scientist and good technologies. As a family we need to know and stay focus of who we are, in what we personally think values stand for because our action wonât always stay of our deepest belief. There is gab between our life values, action and behavior and if we retain those values chances are that even though 50 year from now wonât matter how great the external rewards.

erinhornet739

ADM 2304 Lecture Notes - Lecture 13: Pooled Variance, Type I And Type Ii Errors, Minitab

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