Question

Use the following information to answer the question. Bellei Extravecchio Balsamico Tradizionale is a very expensive brand of balsamic vinegar. A twelve ounce bottle typically costs two-hundred dollars or more. In a blind taste test, a group of food experts tasted three premium balsamic vinegars, with the most expensive one being Bellei Extravecchio Balsamico Tradizionale. When asked to pick the most expensive balsamic vinegar, 92 got it right and 76 got it wrong. Calculate the observed value of the chi-square statistic. Round to the nearest hundredth.

Answer 1

The observed value of the chi-square statistic is 34.71

Explanation:

Given the data in the question';

Calculate the observed value of the chi-square statistic

The chi-square statistic will be;

∑
`_(i)`[ ( O
`_(i)` - E
`_(i)`)² / E
`_(i)` ]

here O
`_(i)` is observed frequency of
`_(i)`th class

E
`_(i)` is expected frequency of
`_(i)`th class

`_(i)` = 1, 2 which denote the class of food experts who guess correctly and who didn't guess correctly

so

∈
`_(i)` = n × probability of not guessing correctly = 168 × 2/3 = 112

∈1 = n × probability of guessing correctly 168 × 1/3 = 56

so

∑
`_(i)`[ ( O
`_(i)` - E
`_(i)`)² / E
`_(i)` ] = [ ( 92 - 56)² / 56 ] + [ ( 76 - 112)² / 112 ]

= 1296/56 + 1296/112

= 23.14 + 11.57

= 34.71

Therefore, the observed value of the chi-square statistic is 34.71