18.05 | Spring 2014 | Undergraduate

Introduction to Probability and Statistics

Readings

Reading Questions 18

Reading Questions Answer Checker

To check your answers put them in the appropriate box and click the ‘Check’ button. Every checker box can do arithmetic and calculate standard functions (see calculator help). If you give decimal answers, give them to at least 3 decimal places.

As you work you should have pencil and paper handy for calculations and thinking!

Note: some questions ask for a formula. For the checker we ask you to plug a value into the formula. For your pset you still need to give the whole formula.

//DEBUG PARAMETERS //Because we don’t show solutions for pset checkers we use //this to give a showanswer button during the debugging phase var debugans = undefined; //release //var debugans = kDebugAnswer; //debug problemNumber = 0; wl("<h3>Calculator</h3>"); writecalculator(“psetcheckcalcid”, “Calculate”); whr(kdivcol,kdivwid);

//Problem 1 problemNumber++; wl(problemheader(problemNumber)); var s; var partName, problemName, buttonLabel, answerArray, correct; s = [“Suppose data is drawn from a normal distribution with unknown mean $μ$ and unknown standard deviation.”, “We make the following hypotheses:”, kbr, “There are 100 points with a sample mean of 2 and sample variance of 36.”, kp, ksp, ksp, “For a one-sample $t$-test let $H_0$: $μ = 1$”, ksp, “and”, ksp, “$H_A$: $μ > 1$.”]; wl(s.join(’ ‘)); wl(kp) s = “(a) What is the value of the $t$ statistic?”; wl(s); wl(kbr); partName = problemNumber + " (a)"; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 5/3, buttonLabel, 0.01, kuseCorrectVal); wl(kp); s = “(b) How many degrees of freedom does the null distribution have?”; wl(s); wl(kbr); partName = problemNumber + " (b)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, 99, buttonLabel, 0.01, kuseCorrectVal); wl(kp); s = “(c) What is the $p$-value for this test? Use R to compute your answer.”; wl(s); wl(kbr); partName = problemNumber + " (c)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; writeNumericBox(partName+“id”, .04937, buttonLabel, 0.002, kuseCorrectVal); wl(kp); s = “(d) At a significance level of $0.01$ do you reject the null hypothesis in favor of $H_A$?”; wl(s); wl(kbr); partName = problemNumber + " (d)”; problemName = “prob” + partName; buttonLabel = “Check problem " + partName; correct = “No”; var answerArray = [‘Yes’,correct]; writeMultipleChoiceRadioGroup(answerArray, problemName, correct, buttonLabel); wl(kp); whr(kdivcol,kdivwid);

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