An Experiment Is Conducted to Investigate How the Behavior of Mozzarella

question 75

Essay

An experiment is conducted to investigate how the behavior of mozzarella cheese varied with temperature. Consider the accompanying data on x = temperature and y = elongation (%) at failure of the cheese. $$\begin{array} { c c c c c c c c } \hline x & 59 & 63 & 67 & 72 & 74 & 78 & 83 \\\hline y & 118 & 182 & 247 & 208 & 197 & 160 & 132 \\\hline\end{array}$$
a. Construct a scatter plot in which the axes intersect at (0,0). Mark 0, 20, 40, 60, 80, and 100 on the horizontal axis and 0, 50, 100, 150, 200, and 250 on the vertical axis.
b. Construct a scatter plot in which the axes intersect at (55,100). Does this plot seem preferable to the one in part (a)? Explain your reasoning.
c. What do the plots of parts (a) and (b) suggest about the nature of the relationship between the two variables?

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Definitions:

Chi-Squared Distributed

Referring to a statistical distribution that is used to describe the distribution of the sum of squares of a set of variables, often used in hypothesis testing.

T-Distribution

A statistical distribution that occurs when calculating the average of a population with a normal distribution, under conditions where the sample size is small and the population's variance is not known.

Degrees of Freedom

The number of independent values or quantities that can vary in a statistical calculation.

Chi-Square Critical Value

A point on the chi-square distribution that is compared to the chi-square test statistic to determine whether to reject the null hypothesis.