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). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? State the type I and type II errors in this case, consequences of each error type for this situation, and the appropriate alpha level to use. 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). Does this data provide enough evidence to show that Alaska had a lower proportion of identity theft than 23%? State the type I and type II errors in this case, consequences of each error type for this situation, and the appropriate alpha level to use.

Answer 1

Here according to federal trade commission report proportion of identity theft is 0.23 &here we have to check that whether it is less than 23% or not .

So our null and alternative hypothesis are

H0: p=0.23 v/s H1: p <0.23

So,In  this case ,

Type 1 error =p (reject Ho when it is true)

=This is equivalent to say that proportion of complaints from identity theft in Alaska are less than 23% when it is actually 23% .

Type 2 error=p (accept Ho when it is false)

=This is equivalent to say that proportion of complaints from identity theft in Alaska are equal to 23% , when it is actually less than 23% .

Consequences of type 1error is that federal commission may think that identity theft is not that big problem as we are thinking & they may ignore the problem of identity theft in alaska when it was actually as big as they had thought. And it is risky .

Consequences of type 2 error is they may think that problem of identity theft in Alaska is as big as we are thinking but actually this wasn't so they may concentrate on this problem more instead of searching and solving other problems. It's simply west of resources .

So, from this two error I came to conclusions that type 1 error is more risky than type 2 error. Since west of resources isn't that risky as compared to ignoring the complaints from identity theft .So  level of significance must be small in that case.we can't ignore more error .

We can take it as 1% .