Question

according to a report on consumer fraud and identity theft, 23% of all complaints during one year were for identity theft. in that year, florida had 323 complaints of identity theft out of 1439 consumer complaints. does this data provide enough evidence to show that florida had a lower proportion of identity theft than 23%? state the random variable, population parameter, and hypotheses. state the random variable. select an answer state the population parameter. select an answer state the hypotheses. $h_0: p$? $square$ $h_a: p$? $square$

Explanation:

Step1: Define random variable

The random variable \(X\) is the number of identity - theft complaints in Florida. In terms of proportion, we can also consider \(X\) as the proportion of identity - theft complaints in Florida out of all consumer complaints in Florida.

Step2: Identify population parameter

The population parameter \(p\) is the proportion of identity - theft complaints in Florida among all consumer complaints in Florida.

Step3: State hypotheses

The null hypothesis \(H_0\) is the status - quo. We assume that the proportion of identity - theft complaints in Florida is the same as the national proportion. The alternative hypothesis \(H_A\) is what we are trying to find evidence for. Since we want to show that Florida has a lower proportion of identity - theft than 23% (or 0.23), we have:
\(H_0:p = 0.23\)
\(H_A:p<0.23\)

Answer:

Random variable: The proportion of identity - theft complaints in Florida out of all consumer complaints in Florida.
Population parameter: The proportion \(p\) of identity - theft complaints in Florida among all consumer complaints in Florida.
\(H_0:p = 0.23\)
\(H_A:p<0.23\)