Question

Consider the following sets of data. Explain (without carrying out a formal Goodness-of-fit test) whether you think the data follows the distribution it is expected to follow. You might choose to find the expected frequencies and compare them with the observed frequencies to make a conclusion. (3 points)

Data Set I: Grades Distribution                                  

Grades	Claimed Distribution	Survey Results
A	10%	20
B	30%	65
C	35%	75
D	10%	17
F	5%	8

Data Set II: Ice-Cream Flavors Preferred

Flavors	Claimed Distribution	Survey Results
Vanilla	10%	80
Chocolate	30%	50
Strawberry	35%	60
Coffee	10%	25
Rainbow	5%	1

  

Data Set III: Type of Credit Card                              

Credit Card	Claimed Distribution	Survey Results
Visa	40%	120
Discover	20%	65
MasterCard	25%	75
American Express	10%	27
Other	5%	10

                                     

Data Set IV: Type of Sport watched

Sports Watched	Claimed Distribution	Survey Results
Baseball	20%	120
Hockey	5%	45
Soccer	25%	75
Football	20%	47
Basketball	30%	100

Answer 1

The expected frequencies can be found by multiply the particular distribution % * total .

Eg. Set 1

A : = 10% * 185 = 18.5

Grades	Claimed		Survey	Expected
Distribution		Results
A	10%		20	18.5
B	30%		65	55.5
C	35%		75	64.75
D	10%		17	18.5
F	5%		8	9.25
Total			185
Here if we see the expected and observed are close to each for 3 of the 5. The remaining have a difference of 10 each. So we can say that the the survey matches with the distribution on some level.
Data Set II: Ice-Cream Flavors Preferred
Flavors	Claimed		Survey	Expected
Distribution		Results
Vanilla	10%		80	21.6
Chocolate	30%		50	64.8
Strawberry	35%		60	75.6
Coffee	10%		25	21.6
Rainbow	5%		1	10.8
Here if we see the expected and observed are very far from each other for all the results. So we can say that the the survey does not match with the distribution on a very high level.
Data Set III: Type of Credit Card
Credit	Claimed		Survey	Expected
Card	Distribution		Results
Visa	40%		120	118.80
Discover	20%		65	59.40
MasterCard	25%		75	74.25
American Express	10%		27	29.70
Other	5%		10	14.85
Here if we see the expected and observed are close to each for almost all the values. The difference is not much. So we can say that the the survey matches with the distribution on high level.
Data Set IV: Type of Sport watched
Sports Watched	Claimed		Survey	Expected
Distribution		Results
Baseball	20%		120	77.4
Hockey	5%		45	19.35
Soccer	25%		75	96.75
Football	20%		47	77.4
Basketball	30%		100	116.1
Here if we see the expected and observed are very far from each other for all the results. So we can say that the the survey does not match with the distribution on a very high level.