mathematics-statistics

profiletademola
Formula-sheet-2.docx
Home>Biology homework help>Anatomy homework help>mathematics-statistics

Formula sheet(Unit 3(

1. Sampling distribution of mean: = N(, /);

Mean = , new standard deviation for sample mean = /

is also called standard error for sample mean

To calculate percent or probability, use

Normalcdf(lower, upper, , /)

2. Sampling distribution of proportion: z = ,

Mean proportion=p

Standard deviation of proportion =

Confidence interval for proportion : Stat, Tests, 1PropZInt 3. Margin of error = E =

Confidence = Middle area, = Invnorm(Left area, 0, 1)

4. Sample size n(How many?)

n =……..Take the next larger number.

5. One sample proportion z test: Stat, tests, 1-PropZTest

6. Student t-distribution for mean:

a. Confidence interval for mean : TInterval

b. Test of hypotheses for mean : TTest

7. Comparing two groups:

a. Comparing two proportions:

(i) Confidence interval: 2PropZInt

(ii)Test of hypotheses : 2PropZTest b. Comparing two means:

(i) Confidence interval : 2SampTInt

(ii)Test of hypotheses: 2SampTTest

8. Paired data: =

Confidence interval: TInterval

Test of hypotheses: TTest

9. Chi Square test:

a. Goodness if fit test : df = n-1

Stat, tests, GOF-Test -------- for column data with frequency

b. Independence test

degree of freedom = df = (r-1)(c-1); [‘r’ means row and ‘c’ means

column]

2nd Matrix, edit. m x n

Stat, Tests, Test --------- for contingency table Expected matrix: 2nd Matrix edit [B] You need to calculate expected matrix after you finish the test. c. Homogeneity test: Same process as independence test except the hypotheses ( ‘same’ or ‘different’ --------------------------------------------------------------------------------------------

Conditions / assumptions : A). For proportion(z distribution)

Sample values are independent, randomized, sample size is less than 10% of the population size, np 10, nq 10 (Check this one) B). For mean(t distribution)

Sample values are independent, randomized Sample size is less than 10% of the population size Distribution is nearly normal.

C). For test: The sampling method is simple random sampling. The variable under study is categorical. Observed values are counts Expected values are at least 5. Notes: If (sigbnificance) is not given, choose it to be 5% (.05)

If Confidence is not given, choose it to be 95% If proportion is not given , choose it to be 0.5 (50%)

P-value < , reject H0

P-value > , do not reject H0

Larger n, smaller error. Smaller n, larger error

Larger confidence, larger error. Smaller confidence, smaller error

z*

z

*

p̂q̂ n

ˆ

p

ˆ

q

n

(z*)2 p̂q̂ (E)2

(z

*

)

2

ˆ

p

ˆ

q

(E)

2

µd

m

d

µ1 −µ2

m

1

-m

2

χ2

c

2

≥

³

χ2

c

2

α

a

n

n

p̂− p pq /n

ˆ

p-p

pq/n