Statistics job interview questions

1. What is difference between Bayesian and Frequentist?
Bayesians condition on the data actually observed and consider the probability distribution on the hypotheses;
Frequentists condition on a hypothesis of choice and consider the probability distribution on the data, whether observed or not.

2. What is likelihood?
The probability of some observed outcomes given a set of parameter values is regarded as the likelihood of the set of parameter values given the observed outcomes.


3. What is p-value and give an example?
In statistical significance testing, the p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true. If the p-value is less than 0.05 or 0.01, corresponding respectively to a 5% or 1% chance of rejecting the null hypothesis when it is true (Type I error).
Example: Suppose that the experimental results show the coin turning up heads 14 times out of 20 total flips
* null hypothesis (H0): fair coin;
* observation O: 14 heads out of 20 flips; and
* p-value of observation O given H0 = Prob(≥ 14 heads or ≥ 14 tails) = 0.115.
The calculated p-value exceeds 0.05, so the observation is consistent with the null hypothesis — that the observed result of 14 heads out of 20 flips can be ascribed to chance alone — as it falls within the range of what would happen 95% of the time were this in fact the case. In our example, we fail to reject the null hypothesis at the 5% level. Although the coin did not fall evenly, the deviation from expected outcome is small enough to be reported as being "not statistically significant at the 5% level".

4. What is sampling? How many sampling methods?
Sampling is that part of statistical practice concerned with the selection of an unbiased or random subset of individual observations within a population of individuals intended to yield some knowledge about the population of concern.
There are four sampling methods: Simple Random (purely random), Systematic( every kth member of population), cluster (population divided into groups or clusters)
and stratified (divided by exclusive groups or strata, sample from each group) samplings.

5. What is the possibility to win lottery game 649?
Pick 6 numbers out of 49 possible. The number of 6-number combination from
a pool of of 49 numbers are:
49!/[(49-6)!6!]=13,983,816
.e We only have one of 14 million chance.

6. what is mode, mean, median, skewness, quartile, variance and standard deviation?
See my old post: Here 


7. What is hypothesis test?
See my old post: Here

8. What is Central Limit Theorem?
See my old post: here

9. Describe Binomial Probability Formula?
See my old post: here