Question

according to a report on consumer fraud and identity theft, 25% of all complaints during one year were for identity theft. in that year, virginia had 327 complaints of identity theft out of 1456 consumer complaints. does this data provide enough evidence to show that virginia had a lower proportion of identity theft than 25%? state the random variable, population parameter, and hypotheses. state the random variable. state the population parameter. state the hypotheses. h0: p = h1: p = > next question

Explanation:

Step1: Define random variable

Let \(X\) be the number of identity - theft complaints in Virginia.

Step2: Identify population parameter

The population parameter is \(p\), the proportion of identity - theft complaints in the entire population of consumer complaints.

Step3: Formulate hypotheses

The null hypothesis \(H_0\) is the status - quo hypothesis. Since the national proportion is \(25\%=0.25\), \(H_0:p = 0.25\). The alternative hypothesis \(H_A\) is what we are trying to find evidence for. We want to show that Virginia has a lower proportion, so \(H_A:p<0.25\).

Answer:

Random variable: \(X\) is the number of identity - theft complaints in Virginia.
Population parameter: \(p\) is the proportion of identity - theft complaints in the population of all consumer complaints.
\(H_0:p = 0.25\)
\(H_A:p<0.25\)