Formulas to know Flashcards
Normal approximation to Binomial
When n is large, Binomial(n, p) gives roughly the same results as…
N (np, np(1 − p))
Use the continuity correction:
for X Binomial and Y Normal,
- P(X > 10) = P(X ≥ 11), but
- P(Y > 10) ≠ P(Y ≥ 11),
so we use P (Y \> 10.5) as a suitable approximation. Similarly P(X \< 10) = P(X ≤ 9) so use P(Y \< 9.5) as an approximation.
Confidence interval for proportions:
Example: in a sample of 100 people, 55 said they were opposed to the Euro. Find a CI for the population proportion.
If X is the number of people in a sample of size n who agree with a given statement, then for large n so that:
X ∼Bin(n,p) ≈ N(np,np(1−p)),
then
p-value=
The p-value is a number between 0 and 1 and interpreted in the following way:
- A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.
- A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.
Statistic test/ t-test=
The t score is a ratio between the difference between two groups and the difference within the groups. The larger the t score, the more difference there is between groups. The smaller the t score, the more similarity there is between groups. A t score of 3 means that the groups are three times as different from each other as they are within each other. When you run a t test, the bigger the t-value, the more likely it is that the results are repeatable.
- A large t-score tells you that the groups are different.
- A small t-score tells you that the groups are similar.
Ignore the minus sign when comparing with t-table