Question

#10. A sample of 500 voters was taken to determine their opinion of a certain newly proposed regulation. Voter were classified on the basis their opinion of the measure and political party affiliation. Results are in the table below: Political Affiliation Opinion Dem Rep Indep Tot For Against Undecided 25 18 21 64 Tot 82 ?7D 62 214 62 67 222 200 150 150 500 An analyst ran a Chi-squared test on the data. (a) What precisely was the null hypothesis being tested? lf the null hypothesis were true how many voters would be expected in the (For, Rep)- cell? 70 (c)How many are actually in the cell? (dyThe test statistic was calculated as 1.53. What would be the conclusion if the test were done at the 10% level of significance?

Answer 1

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Note: In part (b)

$e= \frac{R_i \times C_j}{T}$

Where, $R_i$ corresponds to the total sum of elements in row i, $C_j$ corresponds to the total sum of elements in column j, and T is the grand total.

Row total and column total corresponding to that cell (70) is,

$R_i = 214, \, \, C_j= 150 \, \, \, \text{and} \, \, \, T=500$