STA3022F2018Test1.docx

# In the table below 300 people were asked what bank

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Consider the following contingency table and associated R output. In the table below, 300 people were asked what bank they used most often and to identify the most important reason why they chose that bank. Helpful staff Enjoy advertising Branch close to home Keeps me informed Many ATMs Competitive interest rates TOTAL FNB 14 14 2 23 7 12 72 ABSA 13 6 10 15 5 21 70 NEDBAN K 11 16 8 4 10 8 57 STDBANK 12 14 30 8 28 9 101 TOTAL 50 50 50 50 50 50 300 > ca(bank.data) Principal inertias (eigenvalues): 1 2 3 Value 0.174676 0.046073 0.021778 Percentage 72.02% 19% 8.98% Rows: FNB ABSA NEDBANK STDBANK Mass 0.240000 0.233333 0.190000 0.336667 ChiDist 0.542201 0.468606 0.383164 0.525126 Inertia 0.070556 0.051238 0.027895 0.092838 Dim. 1 -1.172400 -0.794016 0.278962 1.228645 Dim. 2 -0.781987 1.457919 -1.315956 0.289685

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Columns: Branch Competitive Helpful Enjoy close Keeps me Many interest staff advertising to home informed ATMs rates Mass 0.166667 0.166667 0.166667 0.166667 0.166667 0.166667 ChiDist 0.205443 0.400249 0.618174 0.614089 0.516271 0.476418 Inertia 0.007034 0.026700 0.063690 0.062851 0.044423 0.037829 Dim. 1 -0.427021 0.023291 1.378472 -1.336570 1.197046 -0.835218 Dim. 2 -0.278986 -1.788994 1.041542 0.087283 -0.301211 1.240367 (a) Give the average row profile. Show all your calculations. (2) (b) Explain why it is important to compare the row profiles to the average row profile. (2) (c) Give the proportion of inertia accounted for by the two dimensions in the CA map. (1) (d) Give an expression for the Pearson residual associated with cell ( i, j ) . (1) (e) Interpret the CA map given below. (3) (f) What is the hypothesis test associated with simple correspondence analysis. Discuss the test in reference to i. The null and alternative hypothesis (2) ii. Test statistic (1) iii. Degrees of freedom of test statistic (1) iv. Relationships with inertia (1)
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• Summer '17
• Statistics, Statistical hypothesis testing, Sulfur dioxide, free sulfur dioxide, total sulfur dioxide

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