Question

According to the February 2008 Federal Trade Commission report on consumer fraud and identity theft, 23% of all complaints in 2007 were for identity theft. In that year, Alaska had 321 complaints of identity theft out of 1,432 consumer complaints (Consumer fraud and, 2008). (7.1.2)

State the random variable, population parameter, and hypotheses.

Answer 1

Random variable: for this case represent the number of complaints in 2007

Population parameter: represent the real proportion of complaints in 2007 p

Hypothesis to verify

We want to check if the true proportion of complaints in 2007 is equal to 0.23, the system of hypothesis are.:

Null hypothesis:
`p=0.23`

Alternative hypothesis:
`p \\eq 0.23`

Explanation:

Information provided

n=1432 represent the random sample taken

X=321 represent the number of complaints

`\hat p=(321)/(1432)=0.224` estimated proportion of complaints in 2007

`p_o=0.23` is the value to verify

z would represent the statistic

Random variable: for this case represent the number of complaints in 2007

Population parameter: represent the real proportion of complaints in 2007 p

Hypothesis to verify

We want to check if the true proportion of complaints in 2007 is equal to 0.23, the system of hypothesis are.:

Null hypothesis:
`p=0.23`

Alternative hypothesis:
`p \\eq 0.23`