Formulas to know

Question 1

Normal approximation to Binomial

When n is large, Binomial(n, p) gives roughly the same results as…

Answer 1

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.

Question 2

Confidence interval for proportions:

Answer 2

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

Question 3

p-value=

Answer 3

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.

Question 4

Statistic test/ t-test=

Answer 4

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