# Question

Consider a population in which the proportion of members having a specified attribute is p. Let y be the variable whose value is 1 if a member has the specified attribute and 0 if a member does not.

a. If the size of the population is N, how many members of the population have the specified attribute?

b. Use part (a) and Definition 3.11 on page 128 to show that μy = p.

c. Use part (b) and the computing formula in Definition 3.12 on page 130 to show that σy = √p(1 − p).

d. Explain why y = ˆp.

e. Use parts (b)–(d) and Key Fact 7.4 on page 295, to justify Key Fact 11.1.

a. If the size of the population is N, how many members of the population have the specified attribute?

b. Use part (a) and Definition 3.11 on page 128 to show that μy = p.

c. Use part (b) and the computing formula in Definition 3.12 on page 130 to show that σy = √p(1 − p).

d. Explain why y = ˆp.

e. Use parts (b)–(d) and Key Fact 7.4 on page 295, to justify Key Fact 11.1.

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