In: Statistics and Probability
8. 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 55 80 50 35 Outstanding 60 105 65 70 Exceptional 35 65 35 45 Using a level of significance of 0.01, 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? a. State the Null and Alternative hypothesis. b. What is the statistic you would use to analyze this? c. State your decision rule: d. Show your calculation: e. What is your conclusion? Quality Rating and Education level are independent OR Quality Rating and Education level are NOT independent
please show all the work
Chi-Square Test of independence | |||||||
Observed Frequencies | |||||||
some HS | HS grad | some college | college grad | Total | |||
average | 55 | 80 | 50 | 35 | 220 | ||
outstanding | 60 | 105 | 65 | 70 | 300 | ||
exceptional | 35 | 65 | 35 | 45 | 180 | ||
Total | 150 | 250 | 150 | 150 | 700 | ||
Expected frequency of a cell = sum of row*sum of column / total sum | |||||||
Expected Frequencies | |||||||
some HS | HS grad | some college | college grad | Total | |||
average | 150*220/700=47.143 | 250*220/700=78.571 | 150*220/700=47.143 | 150*220/700=47.143 | 220 | ||
outstanding | 150*300/700=64.286 | 250*300/700=107.143 | 150*300/700=64.286 | 150*300/700=64.286 | 300 | ||
exceptional | 150*180/700=38.571 | 250*180/700=64.286 | 150*180/700=38.571 | 150*180/700=38.571 | 180 | ||
Total | 150 | 250 | 150 | 150 | 700 | ||
(fo-fe)^2/fe | some HS | HS grad | some college | college grad | total | ||
average | 1.310 | 0.026 | 0.173 | 3.128 | 4.636 | ||
outstanding | 0.286 | 0.043 | 0.008 | 0.508 | 0.844 | ||
exceptional | 0.331 | 0.008 | 0.331 | 1.0714 | 1.741 |
a)
Ho: customer’s Education level and Quality Rating are independent
Ha: customer’s Education level and Quality Rating are not independent
b) chi square
c) α=0.01
Number of Rows = 3
Number of Columns = 4
Degrees of Freedom=(#row - 1)(#column -1) = (3- 1 ) * ( 4- 1 )
= 6
reject Ho if X² >16.812
d)
Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =
7.222
e) Decision: test statistic,X² < critical value , So, Do not reject the null hypothesis
Quality Rating and Education level are independent