2022-03-04

750 units of product are produced in 3 different production lines. It is desired to investigate whether there is a difference between the production lines at the 95% confidence level. Find the chi-square calculation value.
a. 514
b. 20
c. 45
d. 34

Cypeexorpjng

Chi-Square Test: In statistical hypothesis test, a chi-square test, or specifically Pearson's chi-square test is performed when the test statistic is distributed as chi-square under the null hypothesis. This test is used to determine whether there is a significant difference between the observed and the expected frequencies in one or more categories of a contingency table.
In the standard applications of this test, the observations are classified into mutually exclusive classes. If the null hypothesis is true i.e. there are no significant differences between the classes in the population, the test statistic which is computed from the observations follows a chi-square frequency distribution. The purpose of the test is to determine how likely the observed frequencies would be assuming the null hypothesis is true.
If ${O}_{i}$ and ${E}_{i}$ be the observed and expected frequency for the ${i}^{th}$ category, then the chi-square test statistic is given by,
${\chi }_{c}^{2}=\sum _{i}\frac{{\left({O}_{i}-{E}_{i}\right)}^{2}}{{E}_{i}}$
where c is the degrees of freedom of the chi-square distribution.
Using the given data, we find the chi-square calculation value.
Table for Calculations for Chi-Square

From the table we have,
${\chi }_{c}^{2}=\sum _{i}\frac{{\left({O}_{i}-{E}_{i}\right)}^{2}}{{E}_{i}}=20$