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, assume some state had 362 complaints of identity theft out of 1360 consumer complaints. Do these data provide enough evidence to show that that state had a higher proportion of identity theft than 23%? Test at the 8% level.
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, assume some state had 362 complaints of identity theft out of 1360 consumer complaints. Do these data provide enough evidence to show that that state had a higher proportion of identity theft than 23%? Test at the 8% level.
P: PARAMETER
What is the correct parameter symbol for this problem?
What is the wording of the parameter in the context of this problem?
H: HYPOTHESES
Fill in the correct null and alternative hypotheses:
H0:H0:
HA:HA:
A: ASSUMPTIONS
Since information was collected from each object, what conditions do we need to check?
Check all that apply.
- n≥30n≥30 or normal population.
- N≥20nN≥20n
- n(1−p)≥10n(1-p)≥10
- n(pˆ)≥10n(p̂)≥10
- σσ is unknown.
- np≥10np≥10
- σσ is known.
- n(1−pˆ)≥10n(1-p̂)≥10
Check those assumptions:
1. npnp = which is
2. n(1−p)n(1-p) = which is
3. NN = which is
If no N is given in the problem, use 1000000
N: NAME THE PROCEDURE
The conditions are met to use a .
T: TEST STATISTIC
The symbol and value of the random variable on this problem are as follows:
Leave this answer as a fraction.
=
The formula set up of the test statistic is as follows.:
(Leave any values that were given as fractions as fractions)
z=pˆ−p√p(1−p)n=z=p̂-pp(1-p)n=
( −- )/√((/(( ⋅(1−⋅(1- )) // ))
Final answer for the test statistic from technology.
Round to 2 decimal places:
z =
O: OBTAIN THE P-VALUE
Report to 4 decimal places.
It is possible when rounded that a p-value is 0.0000
P-value =
M: MAKE A DECISION
Since the p-value , we .
S: STATE A CONCLUSION
There significant evidence to conclude
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