Review for the Final Exam :

Measuring Concepts- 9 Sampling - 11 Confidence Interval - 12 Uni variate and Bivariate Hypothesis test - 15 Correlation & Regression - 17

Measuring Concepts

Attitude Measurement

Attitude is a disposition towards an object with respect to place and time (brand, car, clothing e.t.c)

Theory : Attitude predicts behavior

Three components of attitude

Cognitive - EX: Think about Toyota Camry Effective - EX: I like Toyota Camry Behavioral - EX: I want to buy Toyota Camry

Four types of scale

Nominal - Gives the frequency. And also names the category you belong

Ordinal - which one you like more , doesn't tell how much more you like one over other

Interval - Splits it into Intervals , tells you how much more you like one over the other

Ratio - Ratio of one over the other , it has an absolute zero. This scale is not used in Marketing and Social Science.

Different type of scale to measure the attitude

Categorical Scale - classifies things into categories (It is not an interval scale) to see where the object belongs. It is a nominal scale. It has properties of ordinal scale as well.

Semantic Differential Scale - Takes two opposite scenarios and put them on a scale. It differentiates between the semantics of the object ex:(novel ..... usual). It is an ordinal scale.

Numerical Scale - Uses number in between to differentiate the semantic (Novel 1 2 3 4 5 6 7 usual ) . This is also an ordinal scale

Likert Scale - Defines the degree of agree or disagree to something. It is an interval scale

Ex: (Abortion kills .............. Strongly Agree 1 2 3 4 5 6 7 Strongly disagree )

Constant sum scale : Divide 100 points of the scale among given criteria of an object . It is an Interval scale.

ex: Divide Styling, Acceleration and breaking of car into 100 points

Styling - 25 , Acceleration - 50 , Breaking - 25

Decisions related to scale

How to label the scale . Example (using smiley for happy and unhappy for children)

Balanced scale Vs Unbalanced scale

Balanced Scale : Neutral point falls in middle of the scale Unbalanced Scale : Neutral points doesn't fall in middle of the scale.

Here , Shift the neutral point to any one side to balance the scale.

SAMPLING

Probability sample : Probability of everyone's intrusion is known

Random : Probability of including everyone is known and is non-zero Stratified : Follows the same procedure as quota sample. But within

each category we do random sampling. this sampling is more expensive and accurate

Non- Probability samples

Convenience sample : Every participants intrusion is unknown Quota Sample : Divide the population into available categories and

fix a quota for each category (Ex: dividing Clarkson students into business, engg , e.t..c ). and conduct convenience sampling.

Numerical Problems

1) Pizza : What % of days pizza company will sell 110 or more pizzas

Avg : 100 , S.D : 10

Convert to Z- Distribution

Z = x- u / sigma

=> 110 - 100 / 10 = 0.1 ,

z(0.5) = 0.3413

34.13 % of the days they sell 110 pizza or more

Confidence Interval : Determines the range in the population in which the true mean will fall

CI = x bar + - Zcl . sigma/ sq.root (n)

Sigma - Substitute the standard deviation value

n -sample size

Cl - confidence level

EX:

IQ of clarkson students

X bar = 115 , Confidence level = 95 % (Assume 95 % if its not given), so alpha = 0.05

Z(0.4750 , 0.05) = 1.96 , S.D = 10 , Sample size (n) = 100

CI = 115 + - 1.96 * 10 / Sq.root (100) = 115+ - 1.96

Conclusion : Range : 116.96 to 113.04

Interpretation : 95% of the time IQ will fall between the range 113.04 to 116.96

Univariate Hypothesis :

H0 :u = 115

H 1 : u =/ (not equal) = 115

CL = u + - t (a). df . s/ sq.root (n)

a- alpha

S - standard deviation

n - sample size

Df - degrees of freedom : df = n-1

Ex:

n = 25

X bar = 110

S = 10

Df = 25-1 = 24

t (24, 0.05) = 2.064

CL = 115 + - 2.064 * 10 / sq.root (25)

= 115 + - 4.12

Range : 110.88 to 119.12

X bar doesn't fall under the range . Therefore , we reject the null hypothesis and we conclude that Clarkson students' IQ is not equal to 115

Bivariate Hypothesis :

CI = O + - t(a). df. Sx1(bar). Sx2(bar)

df = n1+n2 -2

Sx1(bar). Sx2(bar) = √(n1−1 ) . s12+ (n2−1 ) . s22

2a * √1n1

+ √1n2

CI = O±t(a , df ) . √(n1−1 ) . s12+ (n2−1 ) . s22

2a * √1n1

+ √1n2