Stat Crunch Assignment

| August 30, 2017

uestion
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 possible
bootstrap sample? Explain why it wouldnt be.
a) 48, 55, 43, 61, 39
b) 43, 39, 56, 43, 61
c) 55, 48, 55, 48, 61
d) 39, 39, 39, 39, 39
2. 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 the
population mean, ? Explain why it wouldnt be.
a) 60.01
b) 80.01
c) 55
d) 52
3. Which of the following p-values would provide more evidence in support of the alternate
hypothesis and against the null hypothesis? Explain your answer.

a) 0.15
b) 0.85
c) 0.009
d) 0.05
4. 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 a
randomization 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 of
30 StatCrunch U students and gathered some survey data regarding those students. Use the
StatCrunch 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 3000
resamples.
a) Paste a copy of your distribution here. (With a PC, you can press the control-alt-fn-F11 keys
to 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 your
bootstrap distribution?
6. Suppose you want to compare the amount of credit card debt for males and females. The null
hypothesis for this problem would be no difference in the mean amount of credit card debt for
males and females and the alternate hypotheses would be that there is a difference in mean
amounts of credit card debt. Conduct a randomization test for two means with 3000
randomizations. (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 what
the p-value means.
d) Do you think the data support the null hypothesis of no difference in mean credit card debt
between males and females or the alternate hypothesis that there is a difference? Explain your
answer.

familiarize you with probability using an applet
The applet is a simulation of flipping a fair coin a given number of times and then estimating the
probability 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 relative
frequency approximation of probability says that the probability of an Event A is estimated by
dividing the number of times that Event A occurred by the number of times the trial was
repeated. For example, if you flip a coin 10 times and get 4 heads, then you could estimate the
probability 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 5
below. Record your results, thoughts about your results.
Probability Simulation
1)At the bottom left side of the applet, set n equal to 10 and then check the animate box. Now
click on Flip. Record the number of heads in 10 flips of a coin and the cumulative probability of
a head based on the ten flips. (The cumulative probability is given at the top of the graph.) Is the
number 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 30
flips of the coin. Record the number of heads in 30 flips and the cumulative probability of a head
based on 30 flips. What is the longest string of consecutive heads or tails that you got in the 30
flips? 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 the
number 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 the
cumulative probability of a head now.
5)The Law of Large Numbers states that if an experiment with a random outcome is repeated a
large number of times, the empirical probability of an event is likely to be close to the true
probability. The larger the number of repetitions, the closer together these probabilities are likely
to be Does the coin flipping process you just completed illustrate the Law of Large Numbers?
Why or why not?

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