Chapter 18

Question 1

for a sign test median is < 150 and you have 22 greater than 150 and 5 less than 150, what is the hype test? What are the formulas to use for this

Answer 1

HO: median < 150
since n = 27, we use the following
M = .5 xn
Q = sqrt of .25 x n
z = (x - m)/ Q 

Since M of 13.5 is smaller than 22, we subtract .5 from x which is 22 in order to caclulate z score

z = (21.5 - 13.5) / 2.5981

P-value = 1-.999 = 0.01 (we use 1 - .999, because x is in the upper tail (22 is more than the mean)

Question 2

When calculating z score and p-value, if x (number of plus signs) is greater than the mean, what do we do

Answer 2

x we subtract .5

p-value 1-

Question 3

If you have a question involving the difference of two brand, what kind of question is this? What calculations do you use? HO, P value
n= 9
7 plus signs

Answer 3

binomial
HO: p=.50
n = 9

take the number of plus signs (say 7) and x >7
- add the probabilities up for 7,8 and 9
since it is a two tailed test (p=.5), we times the p-value by 2

Question 4

Question: net sales for 50 largest stock mutual funds show a median of $15.bill. A sample of 10 of the 50 largest bond mutual funds follows. Using the median, can it be concluded that bond mutual funds are Smaller and have fewer net assets than stock mutual?
What would the hyp test be?
How do you calculate p-value n= 9, number of plus signs is 1

Answer 4

HO: Median > 15
convert to p=.50

calculate p-value
- for 0 and + 1 = 0.0196

Question 5

The median annual income for familie-s living in USA is $56,200.  Annual income for 50 families (in thousands) for a sample of 50 families in Chicago. Use the sample data to see if it can be concluded that the families living in Chicago have a median annual income Greater than $56,200.  
31 plus signs
two = signs
What is the hyp test? 
What would the p-value be?

Answer 5

Ho: Median > 56,200
n= 50 - 2 = 48

M = .5x 48 = 24
Q = sqrt .25 (48) = 3.4641

Since 31 Plus signs is more than 24, this is in the uppertail
x = - .5
p = 1 - ??? is this part actually based on HO?

x = 31 - .5 = 30.5

Question 6

for the WIlcoxon signed rank test, what calculations and formulas do we use

Answer 6

1. calculations
   Additive 1 Add 2 Difference Absolute diff, Rank, Sum of plus ranks

Formulas: 
Mt+ = n(n+1) / 4 
QT+ = sqrt (n(n+1) (2n+1) / 24 
P(T+ > signed ranks) 
calculate z value 
- if sum of ranks is more than the Mt, this is an upper tailed test, -.5 for x and pvalue 1 -

Question 7

For the Mann-Whitney-WIlcoxon test, what are the calculations and formulas

Answer 7

for two categories, we rank them both under their own category and then sum up the ranks

we use the first sum of ranks for example w = 34
formulas:
calculate Mean: Mw = 1/2 n1 (n1+n2=1) = 59.5
Qw = sqrt 1/12 n1n2 (n1+n2+1)

Since 34 is less than 59.5, this is a lower tailed test
x = +.5 34+.5 = 34.5

P-value is calculated based on the HO which is that the two pops are equal so =

so we have to multiple p=value x 2

Question 8

What do we use if we have 3 or more populations?

What is the formula do you use?

Answer 8

Kruskal -Wallis test

Question 9

What is the calculations and formula for the Kruskal-Wallis test

Answer 9

1. rank all numbers, then add up each pop’s sum of ranks
   - so we end up with a sum of ranks for each pop

Next we calculate x2 which is
H= [12/ nt(nt+1) [(rank1)^2 / n1 + (rank2)^2/n2 + ….] =3 (nt+1)
the degrees of freedom is k-1

Question 10

What is the spearman rank correlation coefficient calculations and formulas?

Answer 10

pop1 pop 2 difference squared

rs = 1 - (6xsq diff)/ n (n^2-1)
Qrs = sqrt 1/ (n-1)
Z = rs-0 / Qrs
P-value 
- x2 because it is comparing