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ISU STAT 226 - STAT226_Exam1

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Name: Total: 93 + 1 ≈ 95 points Class Section: [1pt.]EXAM II – STAT 226Fall 2016• Show all your work and write complete and coherent answers.• You must show your ISU student ID card or driver’s license if asked.• You should bring to the exam a calculator capable of taking square roots. You may not use yourcellphone as a calculator. You may not share calculators.• Provide units for numerical answers for quantities that have units (e.g., dollars or thousands ofdollars).• Show all of the steps that you used to get your final answer. If you do not show your work you willnot get full credit and no partial credit can be given in the case of incorrect answers.• If you show clearly the steps needed to arrive at a final numerical answer, you will receive full crediteven if the final calculation is not complete. For example Pr(Z ≥ z) = 1 − 0.95 is just as good asPr(Z ≥ z) = 1 − 0.95 = 0.05.• We strongly recommend the use of a pencil (with an eraser) rather than a pen.• Please write as clearly and neatly as possible. If I cannot read your answers, I cannot give you anycredit.• Feel free to ask for more paper if you need more space.Take the time to carefully read all the questions on the exam! GOOD LUCK !!!Form BSolutionI have neither given nor received anyunauthorized aid in completing this examSignedTotal score:Exam II Stat 226 – FORM B Page 21. [43pts.] NYC Taxi: PART I. The New York City Taxi and Limousine Commission recently re-leased a detailed historical dataset on individual taxi trips in the city. A random sample of 40 tripsyielded an average amount charged to the customer per trip as $16.18 and a standard deviation of$10.09. Is there sufficient evidence to claim that the average amount charged to the customer pertrip for all NYC taxi customers is lower than $15? Test this claim at the significance level α = 0.05.The following analysis is performed in JMP:                                                 (A) [3pts.] Describe in words what the population mean represents in the context of the problem.(B) [5pts.] State the corresponding null and alternative hypothesis using proper statistical notation.(C) Calculate the value of the test statistic (round to the nearest 2 decimal places): Show your work here:(D) The associated degrees of freedom for the t-distribution are:Exam II Stat 226 – FORM B Page 3(E) [2pts.] Based on the information given in the JMP output, identify the p-value associated withthe test statistic in part (C):p-value= (F) [2pts.] (Circle one.) Based on the above p-value make a decision about H0. Use a significancelevel of α = 0.05.i. Reject the null hypothesis because the p-value ≤ α.ii. Reject the null hypothesis because the p-value > α.iii. Fail to reject the null hypothesis because the p-value ≤ α.iv.Fail to reject the null hypothesis because the p-value > α. v. We cannot make this decision, we have insufficient information to do so.(G) [4pts.] Based on your decision, write a conclusion in the context of the problem.(H) [2pts.] (Circle one and fill in the blank.) What is the correct interpretation of the abovep-value?i. The probability that the null hypothesis is true is (p-value from part(E)).ii. The probability that the alternative hypothesis is true is (p-value frompart (E)).iii. The probability of seeing an absolute value of the test-statistic at least as extreme as theobserved one is (p-value from part (E)) assuming H0holds true.iv. The probability of seeing a value of the test-statistic at least as large as the observed one is(p-value from part (E)) assuming H0holds true.v.The probability of seeing a value of the test-statistic at least as small as the observed one is (p-value from part (E)) assuming H0 holds true.vi. None of the above.(I) [2pts.] (Circle all that apply.) The statistical inference about the population mean µ waspossible for which of the following reason(s)?i. The standard deviation of the population is known.ii. The sample is a random sample from the population.iii. The data came from a normally distributed population.iv.The sample size is sufficiently large to ensure the CLT (Central Limit Theorem) applies to the sampling distribution of the sample mean.v. Statistical inference can always be done regardless of the underlying population distributionand of the sample size. That is, the CLT is not needed.Exam II Stat 226 – FORM B Page 4(J) [3pts.] Notice that we tested the significance of the population mean. Can we then makeinferences about the price of a specific NYC taxi ride? Explain your answer in detail. (K) [5pts.] Construct a 99% confidence interval for the true average cost of a NYC taxi ride. Showall your work for full credit.(L) [4pts.] Provide an interpretation of the above confidence interval in the context of the data.PART IIFor Part II of the question assume the same context, that is NYC Taxi but treat the followingquestions as independent from PART I.(A) [2pts.] A random sample of 14


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ISU STAT 226 - STAT226_Exam1

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