A Soft Drink Company Is Conducting Research to Select a New

question 633

Essay

A soft drink company is conducting research to select a new design for the can. A random
sample of participants has been selected. Instead of a typical taste test with two different
sodas, they actually give each participant the same soda twice. One drink is served in a
predominantly red can, the other in a predominantly blue can. The order is chosen
randomly. Participants are asked to rate each drink on a scale of 1 to 10. Thus, the company
wishes to test if the color of the can influences the rating. The ratings were recorded for
each participant. The data are shown in the table below. Does this sample indicate that
there is a difference in the ratings? Test an appropriate hypothesis and state your
conclusion. $$\begin{array} { | c | c | c | } \hline \text { Rater } & \text { Red } & \text { Blue } \\\hline 1 & 4 & 6 \\\hline 2 & 7 & 5 \\\hline 3 & 3 & 6 \\\hline 4 & 8 & 9 \\\hline 5 & 5 & 2 \\\hline 6 & 9 & 9 \\\hline 7 & 7 & 10 \\\hline 8 & 5 & 4 \\\hline 9 & 6 & 8 \\\hline 10 & 9 & 7 \\\hline 11 & 8 & 8 \\\hline 12 & 3 & 7 \\\hline 13 & 6 & 5 \\\hline 14 & 8 & 8 \\\hline 15 & 9 & 10 \\\hline 16 & 7 & 6 \\\hline\end{array}$$

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Definitions:

Level of Significance

A threshold in hypothesis testing that determines whether a result is statistically significant.

Random Samples

A portion of a statistical group where every individual within this segment stands an equal chance of selection.

Contingency Table

A type of table in a matrix format that displays the (multivariate) frequency distribution of the variables.

Independence

In probability and statistics, a condition where two events or variables have no influence on each other's occurrence or value.