Question

1.Referring to the the Goodness-of-fit data shown in table 1. The calculated Chi-sq test statistic is

A. 8.0      B. 12    C. 7.85   D.8.75

Table 1

Chi-Squared goodness-of-fit test

H₀: Follows Uniform Distribution

H₁: Does not follow Uniform Distribution

Category        Observed          Expected         Contribution To Chi-Sq

      1                      12                         8                            2.000

      2                      7                           8                            0.125

      3                      2                            8                            4.500

      4                      7                            8                            0.125

      5                      12                         8                            2.000

      6                      8                            8                            0.000

Answer 1

Q.1) From given table we get, Chi-sq test statistic by adding all column values of contribution to Chi-sq.

Chi-square test statistic is,

$\chi^2 = \sum \frac { \text { (Observed - Expected)}^2}{\text { Expected }}$

$\chi^2 = 2.000 + 0.125 + 4.500 + 0.125 + 2.000+0.000$

$\chi^2 = 8.75$

Answer: D) 8.75