Statistics 1

Question 1

Why is the binomial distribution sometimes approximated?

Answer 1

A binomial distribution can be difficult to calculate if there are a large number of trials (n)

Question 2

When is it appropriate to use a Poisson distribution to approximate a binomial distribution?

Answer 2

• There are a large number of trials (n)
• The probability of success (p) is small
• The expected value (np) of the data is less than 10 (np < 10)

Question 3

What conditions have to be met for a data set to have a Poisson distribution?

Answer 3

• There is a constant probability of success
• There is a uniform rate of occurrence
• The data points are randomly distributed

Question 4

When is it appropriate to use a normal distribution to approximate a binomial distribution?

Answer 4

• There are a large number of trials (n)

- The probability of success (p) is roughly 0.5

Question 5

Which distributions continuous and which are discrete?

Answer 5

The binomial and Poisson distribution are discrete, whilst the normal distribution is continuous

Question 6

When is it appropriate to use a normal distribution to approximate a Poisson distribution?

Answer 6

The mean and variance are roughly equal and both greater than 10

Question 7

How is a hypothesis test set up?

Answer 7

• State the variables (number of trials, mean, probrability of success, etc.)
• State the null hypothesis (H0)
• State the alternative hypothesis
• Carry out the test
• …
• Provide the appropriate conclusion to the testing in context to the question

Question 8

How do you identify skew?

Answer 8

The direction in which the tail of the data skew is pointing