Define a Set $S$ Recursively as Follows:
I $\epsilon \in S$ II RECURSION: If

question 20

Essay

Define a set $S$ recursively as follows:
I. BASIS: $\epsilon \in S$
II. RECURSION: If $s$ and $t$ are in $S$ , then
$\begin{array} { l l l l } \text { a. } 0 s \in S & \text { b. } s 0 \in S & \text { c. } 1 s 1 t \in S & \text { d. } s 1 t 1 \in S \end{array}$
III. RESTRICTION: No strings other than those derived from I and II are in $S$ . Use structural induction to prove that every string in $S$ contains an even number of l's.

Apply the normal approximation to the binomial distribution in hypothesis testing.

Understand the conditions for using z-tests in hypothesis testing and confidence interval estimation.

Determine the appropriate sample size for estimating population proportions.

Understand the Central Limit Theorem and its implications for the distributions of sample means and differences between two sample means.

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Definitions:

Gestalt Psychology

A theory of mind that emphasizes the idea that the whole of anything is greater than its parts, focusing on perception in a holistic manner.

African-American Psychologist

refers to psychologists who are of African-American descent and may focus on issues related to race, culture, and identity in their research and practice.

Shaw University

A historically black university located in Raleigh, North Carolina, known for its diverse programs and as the first HBCU in the South.

Virginia State College

A public historically black university located in Petersburg, Virginia, focused on a wide range of academic disciplines.