Business & Finance homework help

1) Descriptive Statistics
a) Central Tendency: Mean, median, mode
b) Variation: std dev, variance, CV = sd/mean
b) Shape: skewness using histograms: hist()
2) Normal distribution
a) Area finding under the curve: Probabality
of some event. e.g. if we randomly pick up a person
from this group, what are the chances, this person’s
age > 25, or salary < 75000, or weight between 150 and
170 lbs. ==> pnorm()
b) Area is given. We wonder cutoff point(s) for area.
==> qnorm()
3) Confidence Intervals
LowerLimit < mu < UpperLimit
LowerLimit = xbar – z*sd/sqrt(n)
UpperLimit = xbar + z*sd/sqrt(n)
90% confidence level -> z=1.68
95% confidence level -> z=1.96
99% confidence level -> z=2.58
For example: qnorm(0.95) = 1.68
4) Hypothesis testing – One sample
Two sided (mu = A or not)
a) Construct your hypothesis
H0: mu = A
Ha: mu != A
b) i) Calculate zcrit and zstat using formulas.
Sketch and look at zstat’s position in the distribution.
ii) Use t.test() function. Look at the pvalue.
5) Hypothesis testing – One sample
One sided (mu > A or not)
a) Construct your hypothesis
H0: mu <= A
Ha: mu > A
H0: mu >= A
Ha: mu < A
b) Same procedure as in two sided except
don’t divide alpha by 2.
If question is “>”, shade the right tail.
If question is “<“, shade the left tail.
6) Hypothesis testing – Two samples
a) Paired t-test: t.test(…, paired = TRUE, ..)
b) Equal variances: t-test(…, var.equal = TRUE,..)
c) Seperate variances t-test: t-test(…, var.equal = FALSE,..)
Look at the pvalue, if it is less than alpha/2, then reject H0.
7) z-test for proportions
One categorical variable. Test claims about the proportion
of one category. e.g. Proportion of voters supporting
candidate A is equal to 55%.
Majority: 50% or more supporting candidate A.
8) Chi-Square test for independence
Two categorical variables. Test if these two variables
are independent or not. Use the chi.square() and look at pvalue.
If pvalue < alpha, reject H0 which says they are independent.
9) ANOVA F test
One numerical and One categorical variable.
You are testing if the mean of the numerical variable differentiate
along the categories of the categorical variable.
H0: mu1 = mu2 = mu3 …. = mun
Ha: At least one mean is different.
Use function aov() and look at pvalue to see if you can reject H0.
10) Linear Regression
Simple Lin. Regression: Y = b0 + b1*X
Multiple Linear Regression: Y = b0 + b2*X1 + b2*X2 + … + bn*Xn
Calculate b coefficients using lm() function.
Make sure the model is a good fit.
Understand what each coefficient means.
 
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