ISU STAT 226 - STAT226_Exam1 (8 pages)

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STAT226_Exam1



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STAT226_Exam1

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Pages:
8
School:
Iowa State University
Course:
Stat 226 - Intr Busines Stat I
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Name Total 93 1 95 points Class Section 1pt EXAM II STAT 226 Fall 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 your cellphone as a calculator You may not share calculators Provide units for numerical answers for quantities that have units e g dollars or thousands of dollars Show all of the steps that you used to get your final answer If you do not show your work you will not 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 credit even if the final calculation is not complete For example Pr Z z 1 0 95 is just as good as Pr 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 any credit 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 B Solution I have neither given nor received any unauthorized aid in completing this exam Signed Total score Exam II Stat 226 FORM B Page 2 1 43pts NYC Taxi PART I The New York City Taxi and Limousine Commission recently released a detailed historical dataset on individual taxi trips in the city A random sample of 40 trips yielded 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 per trip for all NYC taxi customers is lower than 15 Test this claim at the significance level 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 with the test statistic in part C p value F 2pts Circle one Based on the above p value make a decision about H0 Use a significance level of 0 05 i ii iii iv Reject the null hypothesis because the p value Reject the null hypothesis because the p value Fail to reject the null hypothesis because the p value Fail to reject the null hypothesis because the p value 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 above p value p value from part i The probability that the null hypothesis is true is E ii The probability that the alternative hypothesis is true is p value from part E iii The probability of seeing an absolute value of the test statistic at least as extreme as the observed one is p value from part E assuming H0 holds 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 H0 holds 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 was possible for which of the following reason s i ii iii iv The standard deviation of the population is known The sample is a random sample from the population The data came from a normally distributed population 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 distribution and 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 make inferences 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 Show all your work for full credit L 4pts Provide an interpretation of the above confidence interval in the context of the data PART II For Part II of the question assume the same context that is NYC Taxi but treat the following questions as independent from PART I A 2pts A random sample of 14 taxi rides is taken and one of the instructors constructed a 90 confidence interval for the true average cost of a NYC taxi ride based on these 14 observations Explain why the confidence interval should not be used as an estimate for the true mean B 2pts Assume the instructors confidence interval is as follows 12 75 to 18 25 Based on this confidence interval what sample mean did the instructor use C 2pts What standard deviation is the 90 confidence interval ranging from 12 75 to 18 25 based on Show work here Final Answer Exam II Stat 226 FORM B Page 5 2 19pts Game of Thrones During the spring HBO released ten episodes of their flagship show Game of Thrones GOT Many fans watched the new episodes immediately at 8 PM through the streaming service HBO Now or HBO Go However for various reasons many fans had to wait before they could begin watching Analyzing data from all online watchers HBO determined that across all ten episodes of the latest season the mean wait time to begin streaming an episode is 31 9 minutes with a standard deviation 21 1 minutes Due to a number of fans who waited until the following day the distribution of the wait times to begin streaming exhibits a heavy right skew A 3pts Suppose HBO could provide us with the times it took 16 randomly sampled GOT watchers to start watching the 7th episode of last season The Broken Man The corresponding sampling distribution of the sample mean i e the distribution of all sample means based on samples of size 16 from all GOT watchers has the following attributes i Shape Choose one Normal Approximately Normal Not Normal ii Mean 1 pt each DO NOT ROUND B 3pts Suppose now that HBO could provide us with the wait times for 64 randomly sampled GOT …


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