Problem 1

The average number of cavities that thirty-year-old Americans have had in their lifetimes is 9. Do twenty-year-olds have more cavities? The data show the results of a survey of 13 twenty-year-olds who were asked how many cavities they have had. Assume that the distribution of the population is normal.

7, 13, 11, 12, 9, 8, 11, 9, 12, 9, 9, 12, 10

What can be concluded at the = 0.01 level of significance?

1. For this study, we should use Select an answer t-test for a population mean z-test for a population proportion
2. The null and alternative hypotheses would be:

H0:H0: ? p Select an answer < = >

H1:H1: ? p Select an answer < = >

1. The test statistic ? t z = (please show your answer to 3 decimal places.)
2. The p-value = (Please show your answer to 4 decimal places.)
3. The p-value is ? >
4. Based on this, we should Select an answer accept fail to reject reject the null hypothesis.
5. Thus, the final conclusion is that ...The data suggest the population mean is not significantly more than 9 at = 0.01, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is equal to 9.

• The data suggest the populaton mean is significantly more than 9 at = 0.01, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is more than 9.
  • The data suggest that the population mean number of cavities for twenty-year-olds is not significantly more than 9 at = 0.01, so there is insufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is more than
  • 6 .Interpret the p-value in the context of the study. Interpret the level of significance in the context of the stu
    • If the population mean number of cavities for twenty-year-olds is 9 and if you survey another 13 twenty-year-olds then there would be a 2.05593031% chance that the sample mean for these 13 twenty-year-olds would be greater than 10.15.
    • There is a 2.05593031% chance that the population mean number of cavities for twenty-year-olds is greater than 9.
    • If the population mean number of cavities for twenty-year-olds is 9 and if you survey another 13 twenty-year-olds then there would be a 2.05593031% chance that the population mean number of cavities for twenty-year-olds would be greater than 9.
    • There is a 2.05593031% chance of a Type I error.
• 7.Interpret the level of significance in the context of the study.
  • There is a 1% chance that the population mean number of cavities for twenty-year-olds is more than 9.
  • If the population mean number of cavities for twenty-year-olds is more than 9 and if you survey another 13 twenty-year-olds, then there would be a 1% chance that we would end up falsely concuding that the population mean number of cavities for twenty-year-olds is equal to 9.
  • If the population mean number of cavities for twenty-year-olds is 9 and if you survey another 13 twenty-year-olds, then there would be a 1% chance that we would end up falsely concuding that the population mean number of cavities for twenty-year-olds is more than 9.
  • There is a 1% chance that flossing will take care of the problem, so this study is not necessary.

Problem 2

The recidivism rate for convicted sex offenders is 9%. A warden suspects that this percent is higher if the sex offender is also a drug addict. Of the 394 convicted sex offenders who were also drug addicts, 43 of them became repeat offenders. What can be concluded at the = 0.01 level of significance?

1. For this study, we should use Select an answer z-test for a population proportion t-test for a population mean
2. The null and alternative hypotheses would be: Ho: ? p Select an answer = > < (please enter a decimal) H₁: ? p Select an answer > = < (Please enter a decimal)
3. The test statistic ? t z = (please show your answer to 3 decimal places.)
4. The p-value = (Please show your answer to 4 decimal places.)
5. The p-value is ? >
6. Based on this, we should Select an answer reject fail to reject accept the null hypothesis.
7. Thus, the final conclusion is that ...The data suggest the population proportion is not significantly higher than 9% at = 0.01, 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 9%.

• The data suggest the population proportion is not significantly higher than 9% at = 0.01, 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 9%.
• The data suggest the populaton proportion is significantly higher than 9% at = 0.01, 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 9%.

8. Interpret the p-value in the context of the study.

• There is a 9.22% chance that more than 9% of all convicted sex offender drug addicts become repeat offenders.
• There is a 9.22% chance of a Type I error.
• If the population proportion of convicted sex offender drug addicts who become repeat offenders is 9% and if another 394 convicted sex offender drug addicts are surveyed then there would be a 9.22% chance that more than 11% of the 394 convicted sex offender drug addicts in the study will become repeat offenders.
• If the sample proportion of convicted sex offender drug addicts who become repeat offenders is 11% and if another 394 convicted sex offender drug addicts are observed then there would be a 9.22% chance of concluding that more than 9% of all convicted sex offender drug addicts become repeat offenders.

9. Interpret the level of significance in the context of the study.

• There is a 1% chance that Lizard People aka "Reptilians" are running the world.
• If the population proportion of convicted sex offender drug addicts who become repeat offenders is 9% and if another 394 convicted sex offender drug addicts are observed, then there would be a 1% 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 9%.
• There is a 1% chance that the proportion of all convicted sex offender drug addicts who become repeat offenders is higher than 9%.
• If the population proportion of convicted sex offender drug addicts who become repeat offenders is higher than 9% and if another 394 convicted sex offender drug addicts are observed then there would be a 1% 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 9%.