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A Coffeehouse Wishes to See If Customers Have Any Preference χ2\chi ^ { 2 }

question 28

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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. Calculate the chi-square test statistic χ2\chi ^ { 2 } used to test the claim that the probabilities show no preference.
 Brand 12345 Customers 5565183032\begin{array}{l|ccccc}\text { Brand } & 1 & 2 & 3 & 4 & 5 \\\hline \text { Customers } & 55 & 65 & 18 & 30 & 32\end{array}


Definitions:

Neuroblasts

Immature nerve cells that have the potential to develop into fully functioning neurons, essential for the growth and development of the nervous system.

Cranial Nerves

Twelve pairs of nerves that emerge directly from the brain, not the spinal cord, and control sensory and motor functions of the head and neck.

Spinal Nerves

Nerve fibers extending from the spinal cord, carrying motor, sensory, and autonomic signals between the spinal cord and the body.

Neuralgia

Sharp, severe pain along a nerve or group of nerves, often chronic and recurring.

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