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Simulation - When Model Requirements Fail A Bernoulli
Chapter 5, Problem 42AYU(choose chapter or problem)
Simulation - When Model Requirements Fail A Bernoulli random variable is a variable that is either 0 (a failure) or 1 (a success). The probability of success is denoted p.
(a) Use StatCrunch, MINITAB, or some other statistical spreadsheet to generate 1000 Bernoulli samples of size n = 20 with p = 0.15.
(b) Estimate the population proportion for each of the 1000 Bernoulli samples.
(c) Draw a histogram of the 1000 proportions from part (b). What is the shape of the histogram?
(d) Construct a 95% confidence interval for each of the 1000 Bernoulli samples using the normal model.
(e) What proportion of the intervals do you expect to include the population proportion, p? What proportion of the intervals actually captures the population proportion? Explain any differences.
Questions & Answers
QUESTION:
Simulation - When Model Requirements Fail A Bernoulli random variable is a variable that is either 0 (a failure) or 1 (a success). The probability of success is denoted p.
(a) Use StatCrunch, MINITAB, or some other statistical spreadsheet to generate 1000 Bernoulli samples of size n = 20 with p = 0.15.
(b) Estimate the population proportion for each of the 1000 Bernoulli samples.
(c) Draw a histogram of the 1000 proportions from part (b). What is the shape of the histogram?
(d) Construct a 95% confidence interval for each of the 1000 Bernoulli samples using the normal model.
(e) What proportion of the intervals do you expect to include the population proportion, p? What proportion of the intervals actually captures the population proportion? Explain any differences.
ANSWER:Answer :
- Given, n=20 and p=0.15
using excel
> select data - random number generation
> number of variables = 1000 and numbers of random numbers = 20
> select bernoulli distribution and p-value = 0.15
> ok
We will get the sample and some of the samples are shown below
1 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
0 |
1 |