Sampling and the Binomial Distribution. Following is a gender frequency distribution for students in ProfessorWeiss’s introductory statistics class. Gender Frequency Male 17 Female 23 Two students are selected at random. Find the probability that both students are male if the selection is done a. with replacement.b. without replacement.c. Compare the answers obtained in parts (a) and (b).Suppose that Professor Weiss’s class had 10 times the students, but in the same proportions, that is, 170 males and 230 females.d. Repeat parts (a)–(c), using this hypothetical distribution of students.e. In which case is there less difference between sampling without and with replacement? Explain why this is so.
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Sampling and the Binomial Distribution. Following is a gender frequency distribution for students in ProfessorWeiss’s introductory statistics class.
| Gender | Frequency |
| Male | 17 |
| Female | 23 |
Two students are selected at random. Find the probability that both students are male if the selection is done
a. with replacement.
b. without replacement.
c. Compare the answers obtained in parts (a) and (b).
Suppose that Professor Weiss’s class had 10 times the students, but in the same proportions, that is, 170 males and 230 females.
d. Repeat parts (a)–(c), using this hypothetical distribution of students.
e. In which case is there less difference between sampling without and with replacement? Explain why this is so.
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