STATISTICS (ISDS 361A) EXCEL AND REVIEW
1.
Difference Between the
Random Variable X and the Random Variable
X = the outcome of ______
True Mean = ____ True Variance = ____ True Standard Deviation = ____
Distribution of X is either Normal or Not Normal
= the ______outcome of ______
True Mean = ____ True Variance = ____ True Standard Deviation = ____
Distribution of depends on 2 things:
(1) Is X normal (or is the sample (n) large—Central Limit Theorem)?
If NO – the distribution of is ______
(2) If YES, is σ known?
If σ IS known, is ______, Standard Deviation = ______
If σ IS NOT known, is _____, Standard Deviation = ______
It is the distribution of ____ that determines what kind of hypothesis test (z or t) to perform or what confidence interval (z or t) to create.
z-tests and z-intervals when:
(1) X is normal or n is large and (2) σ is ______
t-tests and t-intervals when:
(1) X is normal or n is large and (2) σ is ______
No test or interval if X is not normal and n is small.
2.
Excel Probabilities For a Normal Random Variable X with
mean = μ and standard deviation = σ
Probability of any specific value P(X = a) = ______
Probability to the left: P(X < a) = NORMDIST(______)
Probability to the right: P(X > a) = ______
In Between Probability: P(a < X < b) = ______
x value that puts probability p to the left = NORMINV(______)
x value that puts probability p to the right = NORMINV(______)
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Excel Probabilities for z-values
Probability of any specific value P(z = a) = ______
Probability to the left: P(Z < a) = NORMSDIST(___)
Probability to the right: P(Z > a) = ______
In Between Probability: P(a < Z < b) = ______
z value that puts probability p to the left = NORMSINV(____)
z value that puts probability p to the right = NORMSINV(___)
One z-value we use frequently is z.025.
In Excel, z.025 would be found by NORMSINV(______)
3.
EXCEL CONFIDENCE INTERVALS
General Form of a Confidence Interval
______± ______* ______
______
z-Intervals
Use z intervals when: (1) ______or ______and (2) ______
(1) Get by = ______
(2) Get Lower Confidence Limit (LCL) by ______
Get Upper Confidence Limit (UCL) by ______
t-Intervals
Use t intervals when: (1) ______or ______and (2) ______
(1) Go to Tools/Data Analysis/Descriptive Statistics
(2) Get Lower Confidence Limit (LCL) by ______
Get Upper Confidence Limit (UCL) by ______
Note: the t-value that puts probability α/2 to the right, tα/2 = ______
So another way to get the margin of error (Confidence) is ______
4.
EXCEL HYPOTHESIS TESTS
Greater Than TestsLess Than TestsNot Equal Tests
H0: μ = v H0: μ = v H0: μ = v
HA: μ > v HA: μ < v HA: μ ≠ v
What you are trying to show is true is: ______
First calculate ____
A test statistic (z or t) is______
(______) – (______)
Form of test statistic: ______
(______)
A p-value is: > test ______
It is the area ______
< test ______
It is the area ______
≠ test ______
It is the 2*area ______
If a p-value is low, H0 is very unlikely to be true thus we reject H0 and Accept HA. Thus, LOW p-values are ______!
CALCULATION OF EXCEL p-VALUES
First, in a cell calculate z = ______, or t = ______
Get values from Descriptive Statistics
> Tests / < Tests / ≠ Testsz-test p-value
t-test p-value
Note: TDIST(t,DF,1) gives the area to the right of t; and t must be positive.