An Observed Frequency Distribution Is as Follows $\begin{array}{l|ccc}\text { Number of successes } & 0 & 1 & 2 \\\hline \text { Frequency } & 41 & 93 & 66\end{array}$

question 24

Essay

An observed frequency distribution is as follows: $\begin{array}{l|ccc}\text { Number of successes } & 0 & 1 & 2 \\\hline \text { Frequency } & 41 & 93 & 66\end{array}$
i) Assuming a binomial distribution with $\mathrm { n } = 2$ and $\mathrm { p } = 1 / 2$ , 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 $\mathrm { n } = 2$ and $\mathrm { p } = 1 / 2$ .

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Definitions:

Per Share

A financial metric that represents some quantity divided by the total number of outstanding shares of a company, often used in financial ratios.

First-day Returns

The percentage change in price of a stock or other security from its offering price on its first day of public trading.

SIPC

SIPC stands for the Securities Investor Protection Corporation, which is a nonprofit organization that insures investors' securities and cash in the event a brokerage firm goes bankrupt or faces financial difficulties.

Brokerage Firm

A company that acts as an intermediary between buyers and sellers of financial securities, providing investment services and advice.