## Stat Crunch Assignment

Answer each of the following questions.1. If the original sample is 48, 55, 43, 61, 39, which of the following would not be a possiblebootstrap sample? Explain why it wouldnt be.a) 48, 55, 43, 61, 39b) 43, 39, 56, 43, 61c) 55, 48, 55, 48, 61d) 39, 39, 39, 39, 392. The following bootstrap output is for mileage of a random sample of 25 mustang cars.Based on a 90% confidence interval, which of the following would not be a plausible value of thepopulation mean, ? Explain why it wouldnt be.a) 60.01b) 80.01c) 55d) 523. Which of the following p-values would provide more evidence in support of the alternatehypothesis and against the null hypothesis? Explain your answer.a) 0.15b) 0.85c) 0.009d) 0.054. In a sample of 56 addicts, 28 were given a new drug to help them overcome their addiction,while the remaining 28 were given the current drug. The following is the output from arandomization test for the difference in the proportion of addicts suffering relapses.a) What is the difference in proportions in the original data?b) What is the p-value and what does it mean in terms of this specific problem?In StatCrunch Assignment (the one you have done already) you selected a random sample of30 StatCrunch U students and gathered some survey data regarding those students. Use theStatCrunch data file you created to complete the remainder of this assignment.5. Construct a bootstrap distribution of the credit card debt data from your sample using 3000resamples.a) Paste a copy of your distribution here. (With a PC, you can press the control-alt-fn-F11 keysto copy the window showing the distribution.)b) What is the mean of your original sample?c) What is the 95% confidence interval estimate of the population mean obtained from yourbootstrap distribution?6. Suppose you want to compare the amount of credit card debt for males and females. The nullhypothesis for this problem would be no difference in the mean amount of credit card debt formales and females and the alternate hypotheses would be that there is a difference in meanamounts of credit card debt. Conduct a randomization test for two means with 3000randomizations. (Your input menu should be as follows.)a) Paste the output from your randomization test here.b) What is the mean difference in credit card debt of the two groups in the original data?c) What p-value did you get in your randomization? Explain in the context of the problem whatthe p-value means.d) Do you think the data support the null hypothesis of no difference in mean credit card debtbetween males and females or the alternate hypothesis that there is a difference? Explain youranswer.familiarize you with probability using an appletThe applet is a simulation of flipping a fair coin a given number of times and then estimating theprobability of getting a head using the relative frequency approximation of probability.The probability of getting a head or tail on one flip of a fair coin is 0.5 or 50%. The relativefrequency approximation of probability says that the probability of an Event A is estimated bydividing the number of times that Event A occurred by the number of times the trial wasrepeated. For example, if you flip a coin 10 times and get 4 heads, then you could estimate theprobability of getting a head as 4 divided by 10 or 0.4.Use the the probability simulation, hyperlink to access the applet and follow steps 1 through 5below. Record your results, thoughts about your results.Probability Simulation1)At the bottom left side of the applet, set n equal to 10 and then check the animate box. Nowclick on Flip. Record the number of heads in 10 flips of a coin and the cumulative probability ofa head based on the ten flips. (The cumulative probability is given at the top of the graph.) Is thenumber of heads what you expected in 10 flips?2)Now uncheck the animate box and click on flip two more times. You should now have 30flips of the coin. Record the number of heads in 30 flips and the cumulative probability of a headbased on 30 flips. What is the longest string of consecutive heads or tails that you got in the 30flips? Do you think that is unusual?3)Now set n to 1000 and click on flip. This should give you 1030 flips of the coin. Record thenumber of heads and the cumulative probability of a head now.4)Click on flip one more time so that you have 2030 flips. Record the number of heads and thecumulative probability of a head now.5)The Law of Large Numbers states that if an experiment with a random outcome is repeated alarge number of times, the empirical probability of an event is likely to be close to the trueprobability. The larger the number of repetitions, the closer together these probabilities are likelyto be Does the coin flipping process you just completed illustrate the Law of Large Numbers?Why or why not?

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