Answer:
The answer is 37.45
Step-by-step explanation:
The distribution is uniform so expected value of each brand is
E = 200/5
E = 40
Chi Square statistic is
[tex]x^2 = \frac{(30-40)^2}{40} +\frac{(65-40)^2}{40} + \frac{(18-40)^2}{40} + \frac{(39-40)^2}{40} + \frac{(55-40)^2}{40}[/tex]
[tex]x^2=\frac{100+625+484+64+225}{40}[/tex]
[tex]x^2=\frac{1498}{40}[/tex]
[tex]x^2= 37.45[/tex]
Hence, the chi-square test statistic χ2 to test the claim that the distribution is uniform is 37.45
This question is based on the concept of statistics. Therefore, the chi-square test statistic χ2 to test the claim that the distribution is uniform is 37.45. Hence, the correct option is B.
Given:
A coffeehouse wishes to see if customers have any preference among 5 different brands of coffee. A sample of 200 customers provided the data below.
We need to calculate the chi-square test statistic [tex]X^2[/tex]to test the claim that the distribution is uniform.
According to the question,
The distribution is uniform, then, the expected value of each brand is,
[tex]E = \dfrac{200}{5}\\\\E = 40[/tex]
As we know that, Chi Square statistic is,
[tex]\chi ^2 = \dfrac{(30-40)^2}{40} +\dfrac{(65-40)^2}{40} + \dfrac{(18-40)^2}{40} +\dfrac{(39-40)^2}{40} +\dfrac{(55-40)^2}{40}[/tex]
[tex]\chi^2 = \dfrac{100+625+484+64+225}{40}\\\\\chi^2 = \dfrac{1498}{40} \\\\\chi^2 = 37.45[/tex]
Therefore, the chi-square test statistic χ2 to test the claim that the distribution is uniform is 37.45. Hence, the correct option is B.
For further details, prefer this link:
https://brainly.com/question/2365682
