The recidivism rate for convicted sex offenders is 16%. A warden suspects that this percent is higher if the sex offender is also a drug addict. Of the 378 convicted sex offenders who were also drug addicts, 72 of them became repeat offenders. What can be concluded at the a = 0.10 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: ? v Select an answer v (please enter a decimal) H1:? v Select an answer ♥ (Please enter a decimal) c. The test statistic ? v = (please show your answer to 3 decimal places.) d. The p-value = | (Please show your answer to 4 decimal places.) e. The p-value is ? v a f. Based on this, we should Select an answer v the null hypothesis. g. Thus, the final conclusion is that ... The data suggest the population proportion is not significantly higher than 16% at a = 0.10, so there is statistically significant evidence to conclude that the population proportion of convicted sex offender drug addicts who become repeat offenders is equal to 16%. O The data suggest the population proportion is not significantly higher than 16% at a = 0.10, so there is statistically insignificant evidence to conclude that the population proportion of

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The recidivism rate for convicted sex offenders is 16%. A warden suspects that this percent is higher if the
sex offender is also a drug addict. Of the 378 convicted sex offenders who were also drug addicts, 72 of
them became repeat offenders. What can be concluded at the a =
0.10 level of significance?
a. For this study, we should use Select an answer
b. The null and alternative hypotheses would be:
Ho: ? v Select an answer
(please enter a decimal)
H1:? v Select an answer
(Please enter a decimal)
c. The test statistic ? v =
(please show your answer to 3 decimal places.)
d. The p-value
(Please show your answer to 4 decimal places.)
e. The p-value is ? v a
f. Based on this, we should Select an answer v the null hypothesis.
g. Thus, the final conclusion is that ...
O The data suggest the population proportion is not significantly higher than 16% at a = 0.10, so
there is statistically significant evidence to conclude that the population proportion of
convicted sex offender drug addicts who become repeat offenders is equal to 16%.
The data suggest the population proportion is not significantly higher than 16% at a = 0.10, so
there is statistically insignificant evidence to conclude that the population proportion of
convicted sex offender drug addicts who become repeat offenders is higher than 16%.
O The data suggest the populaton proportion is significantly higher than 16% at a = 0.10, so
there is statistically significant evidence to conclude that the population proportion of
convicted sex offender drug addicts who become repeat offenders is higher than 16%.
Transcribed Image Text:The recidivism rate for convicted sex offenders is 16%. A warden suspects that this percent is higher if the sex offender is also a drug addict. Of the 378 convicted sex offenders who were also drug addicts, 72 of them became repeat offenders. What can be concluded at the a = 0.10 level of significance? a. For this study, we should use Select an answer b. The null and alternative hypotheses would be: Ho: ? v Select an answer (please enter a decimal) H1:? v Select an answer (Please enter a decimal) c. The test statistic ? v = (please show your answer to 3 decimal places.) d. The p-value (Please show your answer to 4 decimal places.) e. The p-value is ? v a f. Based on this, we should Select an answer v the null hypothesis. g. Thus, the final conclusion is that ... O The data suggest the population proportion is not significantly higher than 16% at a = 0.10, so there is statistically significant evidence to conclude that the population proportion of convicted sex offender drug addicts who become repeat offenders is equal to 16%. The data suggest the population proportion is not significantly higher than 16% at a = 0.10, so there is statistically insignificant evidence to conclude that the population proportion of convicted sex offender drug addicts who become repeat offenders is higher than 16%. O The data suggest the populaton proportion is significantly higher than 16% at a = 0.10, so there is statistically significant evidence to conclude that the population proportion of convicted sex offender drug addicts who become repeat offenders is higher than 16%.
h. Interpret the p-value in the context of the study.
O If the population proportion of convicted sex offender drug addicts who become repeat
offenders is 16% and if another 378 convicted sex offender drug addicts are surveyed then
there would be a 5.3% chance that more than 19% of the 378 convicted sex offender drug
addicts in the study will become repeat offenders.
O If the sample proportion of convicted sex offender drug addicts who become repeat offenders
is 19% and if another 378 convicted sex offender drug addicts are observed then there would
be a 5.3% chance of concluding that more than 16% of all convicted sex offender drug addicts
become repeat offenders.
There is a 5.3% chance of a Type I error.
There is a 5.3% chance that more than 16% of all convicted sex offender drug addicts become
repeat offenders.
i. Interpret the level of significance in the context of the study.
O If the population proportion of convicted sex offender drug addicts who become repeat
offenders is 16% and if another 378 convicted sex offender drug addicts are observed, then
there would be a 10% chance that we would end up falsely concluding that the proportion of
all convicted sex offender drug addicts who become repeat offenders is higher than 16%.
There is a 10% chance that Lizard People aka "Reptilians" are running the world.
O If the population proportion of convicted sex offender drug addicts who become repeat
offenders is higher than 16% and if another 378 convicted sex offender drug addicts are
observed then there would be a 10% chance that we would end up falsely concluding that the
proportion of all convicted sex offender drug addicts who become repeat offenders is equal to
16%.
There is a 10% chance that the proportion of all convicted sex offender drug addicts who
become repeat offenders is higher than 16%.
Transcribed Image Text:h. Interpret the p-value in the context of the study. O If the population proportion of convicted sex offender drug addicts who become repeat offenders is 16% and if another 378 convicted sex offender drug addicts are surveyed then there would be a 5.3% chance that more than 19% of the 378 convicted sex offender drug addicts in the study will become repeat offenders. O If the sample proportion of convicted sex offender drug addicts who become repeat offenders is 19% and if another 378 convicted sex offender drug addicts are observed then there would be a 5.3% chance of concluding that more than 16% of all convicted sex offender drug addicts become repeat offenders. There is a 5.3% chance of a Type I error. There is a 5.3% chance that more than 16% of all convicted sex offender drug addicts become repeat offenders. i. Interpret the level of significance in the context of the study. O If the population proportion of convicted sex offender drug addicts who become repeat offenders is 16% and if another 378 convicted sex offender drug addicts are observed, then there would be a 10% chance that we would end up falsely concluding that the proportion of all convicted sex offender drug addicts who become repeat offenders is higher than 16%. There is a 10% chance that Lizard People aka "Reptilians" are running the world. O If the population proportion of convicted sex offender drug addicts who become repeat offenders is higher than 16% and if another 378 convicted sex offender drug addicts are observed then there would be a 10% chance that we would end up falsely concluding that the proportion of all convicted sex offender drug addicts who become repeat offenders is equal to 16%. There is a 10% chance that the proportion of all convicted sex offender drug addicts who become repeat offenders is higher than 16%.
Expert Solution
Step 1

Given :

x = 72

n = 378

p^ = xn

p^ = 72378

p^ = 0.191

α = 0.1

a)

For this study, we should use one-sample proportion test.

b)

H0 :p = 0.16

H1 :p > 0.16

Step 2

c) Test Statistic :

z = 0.191-0.160.16×0.84378

z = 0.03050.0189

z = 1.616

d)

P-value  = 0.053

e)

P-value is less than α.

f)

Based on this , we should reject the null hypothesis.

g)

C. The data suggest the population proportion is significantly higher than  16% at α = 0.10, so there is statistically significant evidence to conclude that the population proportion ofconvicted sex offender drug addicts who become repeat offenders is higher than 16%.

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