Solved by verified expert:Login and complete midterm…will provide login details…really need an A on this assignmentMUST USE SCRACTH PAPER AND UPLOAD PICTURE OF WORK ONCE COMPLETE WITH THE TEST FOR THE PROFESSORSEND IT HERE AND I WILL SEND TO THE PROFESSORMUST ONLY USE THE FORMULAS AND SYMBOLS FROM THE ATTACHED WORKSHHET FROM THE COURSETEST IS TIMES FOR TWO HOURS

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X, Y

variables

n

number of people in a research group or sample

N

number of people in target population

ρ

rho (pronounced row)

Σ

sum (sigma)

μ

populational mean (pronounced mu)

M

sample mean (pronounced x bar)

α

alpha

β

beta

≥

greater than or equal to

≤

less than or equal to

σ

populational standard deviation (sigma)

s

sample standard deviation (also will see the symbol, SD)

±

plus/minus

Order of Mathematical Operations

1.

Parentheses (innermost to outermost)

Exponents

2.

3.

Multiplying/dividing

4.

Summation (Σ)

5.

Adding/subtracting

Example:

3(X2-2XY)(2+7X2+X)2+2

(X-Y)(Y-X2)

What order would you do the calculations?

If x = 2 & y = 3

Descriptive Statistics Formula Sheet

Sample

Population

Characteristic

statistic

Parameter

raw scores

x, y, . . . . .

X, Y, . . . . .

mean (central tendency)

M=

μ=

range (interval/ratio data)

∑x

n

highest minus lowest value

deviation (distance from mean)

Deviation = (x − M )

Deviation = (X − μ )

average deviation (average

∑(x − M )

=0

n

∑(X − μ )

N

(∑ x)2

SS = ∑ x −

n

(∑ x)2

∑ x2 −

n = SS

s2 =

n−1

df

(∑ X)2

SS = ∑ X −

N

(∑ X)2

∑ X2 −

N

σ2 =

N

distance from mean)

sum of the squares (SS)

(computational formula)

variance ( average deviation2 or

2

standard deviation )

(computational formula)

2

standard deviation (average

deviation or distance from mean)

(computational formula)

Z scores (standard scores)

s=

Z=

∑X

N

highest minus lowest value

2

(∑ x)2

n

n−1

σ=

x−M

deviation

=

s

stand. dev.

Z=

2

√∑ x −

mean = 0

standard deviation = ± 1.0

X = M + Zs

Area Under the Normal Curve

(∑ X)2

N

N

2

√∑ X −

X−μ

σ

X = μ + Zσ

-1s to +1s = 68.3%

-2s to +2s = 95.4%

-3s to +3s = 99.7%

Using Z Score Table for Normal Distribution

(Note: see graph and table in A-23)

for percentiles (proportion or %) below X

for positive Z scores – use body column

for negative Z scores – use tail column

for proportions or percentage above X

for positive Z scores – use tail column

for negative Z scores – use body column

to discover percentage / proportion between two X values

1. Convert each X to Z score

2. Find appropriate area (body or tail) for each Z score

3. Subtract or add areas as appropriate

4. Change area to % (area × 100 = %)

Regression lines

(central tendency line for all

points; used for predictions

only) formula uses raw

scores

b = slope

a = y-intercept

y = bx + a

(plug in x

to predict y)

b=

(∑ x)(∑ y)

n

(∑

x)2

∑ x2 −

n

∑ xy −

a = My – bMx

where My is mean of y

and Mx is mean of x

SEest (measures accuracy of predictions; same properties as standard deviation)

Pearson Correlation Coefficient

(used to measure relationship;

uses Z scores)

r=

r=

(∑ x)(∑ y)

n

2

2

(∑

x)

2 −(∑ y) )

√(∑ x2 −

y

)(∑

n

n

degree x & 𝑦 𝑣𝑎𝑟𝑦 𝑡𝑜𝑔𝑒𝑡ℎ𝑒𝑟

degree x & 𝑦 𝑣𝑎𝑟𝑦 𝑠𝑒𝑝𝑎𝑟𝑎𝑡𝑒𝑙𝑦

r2 = estimate or % of accuracy of predictions

∑ xy−

…

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