binomial distribution

What are the 4 requirements for it to be binomial?

• Fixed number of trials

• Independent events

• Two outcomes

• Same probability

How do you find probabilities on the calculator?

Home - > distribution - > binomial DD - > variable - > x, n, p

How do you use the number line for inequality questions?

Always pick the number to the left of the line

What symbol can the calculator ONLY do?

≤ “less than or equal to “

How do you calculate the mean of a binomial?

N x p

How do you calculate the variance of the binomial?

N x p x (1-p)

What two factors must be true for a test for probability /proportion?

• The sample must be random

• The population must follow the FITS criteria

What are the 6 steps to a binomial proportion test?

Step 1

H0: p = ⋯

H1: p < > ≠ ⋯

Step 2

X ~ B(n, p)

Step 3

The test statistic is the observed value based on the sample

e.g. 2 out of 25, 2 is the test statistic

Step 4

Critical values are found:

• Using the distribution X ~ B(n, p) the p is ALWAYS the one in H0

• Binomial CD function on your calculator

Two tail test ⇒ SPLIT the significance level and find both critical regions

Lower tail: look for significance level

Upper tail: look for 1 – significance level

Step 5

Compare are Reject/Do not Reject H0

Step 6

Conclusion an d Context “proportion”