Question

Please label and show each step A quality survey asked recent customers of their experience at...

Please label and show each step

  1. A quality survey asked recent customers of their experience at a local department store. One question asked for the customers rating on their service using categorical responses of average, outstanding, and exceptional. Another question asked for the applicant’s education level with categorical responses of Some HS, HS Grad, Some College, and College Grad. The sample data below are for 700 customers who recently visited the department store.

Education

Quality Rating

Some HS

HS Grad

Some College

College Grad

Average

50

35

55

80

Outstanding

65

70

60

105

Exceptional

35

45

35

65

Using a level of significance of 0.05, is there evidence to suggest that the customer’s Education level and Quality Rating are independent? In other words, is there a relationship or is there NO relationship between Education and Quality Rating?

  1. State the Null and Alternative hypothesis.

  1. What is the statistic you would use to analyze this?
  1. State your decision rule:

  1. Show your calculation:
  1. What is your conclusion?

Quality Rating and Education level are independent

OR

Quality Rating and Education level are NOT independent

0 0
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Answer #1

(a)

H0: Quality Rating and Education are independent

H1: Quality Rating and Education are not independent

(b)

chi^2 statistic will be analysed here.

(c)

If,

XcalculatedXadf,

Then we reject the null hypothesis

(d)

Original Table with marginal totals:

Some HS HS Grad Some College College Grad Total (f.j)
Average 50 35 55 80 220
Outstanding 65 70 60 105 300
Exceptional 35 45 35 65 180
Total (fi.) 150 150 150 250 700 = f..

Table for,

rac{f_{ij}^2}{f_{i.} * f_{.j}}

Some HS HS Grad Some College College Grad Total
Average 0.076 0.037 0.092 0.116 0.321
Outstanding 0.094 0.109 0.08 0.147 0.43
Exceptional 0.045 0.075 0.045 0.094 0.259
Total 0.215 0.221 0.217 0.357 1.01

So, the value of chi-squared statistic is 700*(1.01-1) = 7 and the corresponding degrees of freedom is (3-1)*(4-1) = 6.

Now, critical value at 5% level of significance is . Since the calculated value is less that the critical value 0.05.6 12.592 , we fail to reject the null hypothesis. Hence, there is insufficient evidence to conclude that Quality Rating and Education are related.

(e)

Quality Rating and Education are independent.

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