Use a ?² Test to Test the Claim That in the Given

question 10

Essay

Use a ?² test to test the claim that in the given contingency table, the row variable and the column variable are independent
-An observed frequency distribution is as follows: $$\begin{array} { l | l l l } \text { Number of successes } & 0 & 1 & 2 \\\hline \text { Frequency } & 41 & 93 & 66\end{array}$$ i)Assuming a binomial distribution with n = 2 and p = 1/2, use the binomial formula to find the probability corresponding to each category of the table. ii)Using the probabilities found in part (i), find the expected frequency for each category. iii)Use a 0.05 level of significance to test the claim that the observed frequencies fit a binomial distribution for which n = 2 and p = 1/2.

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Definitions:

Ppm

Stands for "parts per million," a unit of concentration often used in chemistry and environmental science to describe small amounts of a substance in a larger matrix.

NMR Data

Refers to the information obtained from Nuclear Magnetic Resonance spectroscopy, which is used to determine molecular structure and dynamics.

Triplet

A signal in NMR spectroscopy that is split into three peaks, suggesting an atom's hydrogen atoms are coupled to two equivalent neighboring hydrogens.

Broad Singlet

A NMR signal appearing as a single peak but broader than typical singlets, often resulting from molecules with rapid internal motion.