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HW - June 2 2010 1 Choose a null hypothesis E[X = H0 for...

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June 2, 2010 1. Choose a null hypothesis E[ X ] = μ H 0 for problem 1 of the last homework. Test your null hypothesis at the α = . 10 signiﬁcance level using a classical testing procedure (i.e., without the use of conﬁdence intervals). What do you conclude? 2. Return to problem 3 on the previous homework. Test H 0 : E[ X ] = E[ V ] at the α = . 01 signif- icance level using a classical testing procedure (i.e., without the use of conﬁdence intervals). What do you conclude? You have made two major assumptions in carrying out this test – one involving the CLT and one involving the population variances – what are your assumptions? 3. Prove that if some μ H 0 is not in a 95% conﬁdence interval, then it will be rejected by a classical two-sided test at the α = . 05 level. Do you conclude that (1 - α )% conﬁdence intervals are equivalent to two-sided α level tests? 4. Busy work: For each of the book problems on the last homework assignment, what was the set of plausible (e.g., those that would not be rejected at the α = . 05 signiﬁcance level) hypothesis found? 5. Book problems. .. second to last major problem set for the last test. .. 9-4 9-5 9-7 9-8 9-9 9-12 9-13 9-14 9-15 9-16 9-18 9-23 9-24 9-25 9-26 6. A few old problems that are good to do. .. 7-3 7-7 7-10 7-15 1

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June 1, 2010 1. Give a 90% conﬁdence interval for the population mean E[X] of a variable X in your data. Interpret the interval – both in its statistical properties, and in its meaning for your data. 2. What are the degrees of freedom ( df ) associated with a conﬁdence interval for the diﬀerence of two population means (i.e., E[ X ] - E[ Y ]) when we do not assume Var[ X ] = Var[ Y ]? WIKI! 3. Divide your variable X from problem 1 into two groups on the basis of some other relevant feature in your data, i.e., make one group the ‘treated’ group and the other the ‘control’ group. What is the ‘treatment’? Is there a potential for confounding, i.e., are there diﬀerences between the treated and control groups other than the treatment? Give a 99% conﬁdence interval for the diﬀerence in population means of the treated group and the control group. You have made two major assumptions in creating this interval – one involving the CLT and one involving the population variances – what are your assumptions? 4. Suppose X i binomial( N,p ). What does ¯ x estimate? In a usual setting, do you think you will need to estimate N , or will it be known? How will you estimate p ? Provide two ways to estimate Var[ X ] from a sample X 1 , ··· ,X n . Hint: What is Var[ X ] in this setting? 5. Book problems. .. like what you might could have to do for the test. .. 8-2
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HW - June 2 2010 1 Choose a null hypothesis E[X = H0 for...

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