The average number of cavities that thirty-year-old Americans have had in their lifetimes is 5. Do twenty-year-olds have fewer cavities? The data show the results of a survey of 12 twenty-year-olds who were asked how many cavities they have had. Assume that the distribution of the population is normal.

5, 4, 5, 6, 5, 5, 3, 5, 3, 3, 6, 4

What can be concluded at the = 0.10 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 Correct
2. The null and alternative hypotheses would be:

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

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

1. The test statistic ? t z Correct = Correct (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 reject fail to reject accept the null hypothesis.
5. Thus, the final conclusion is that ...
6. Interpret the p-value in the context of the study.
7. Interpret the level of significance in the context of the study.

• If the population mean number of cavities for twenty-year-olds is less than 5 and if you survey another 12 twenty-year-olds, then there would be a 10% chance that we would end up falsely concuding that the population mean number of cavities for twenty-year-olds is equal to 5.
• There is a 10% chance that flossing will take care of the problem, so this study is not necessary.
• If the population mean number of cavities for twenty-year-olds is 5 and if you survey another 12 twenty-year-olds, then there would be a 10% chance that we would end up falsely concuding that the population mean number of cavities for twenty-year-olds is less than 5.
• There is a 10% chance that the population mean number of cavities for twenty-year-olds is less than 5.

• If the population mean number of cavities for twenty-year-olds is 5 and if you survey another 12 twenty-year-olds, then there would be a 6.97049919% chance that the sample mean for these 12 twenty-year-olds would be less than 4.5.
• If the population mean number of cavities for twenty-year-olds is 5 and if you survey another 12 twenty-year-olds, then there would be a 6.97049919% chance that the population mean number of cavities for twenty-year-olds would be less than 5.
• There is a 6.97049919% chance of a Type I error.
• There is a 6.97049919% chance that the population mean number of cavities for twenty-year-olds is less than 5.

• The data suggest that the population mean number of cavities for twenty-year-olds is not significantly less than 5 at = 0.10, so there is insufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is less than 5.
• The data suggest the populaton mean is significantly less than 5 at = 0.10, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is less than 5.
• The data suggest the population mean is not significantly less than 5 at = 0.10, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is equal to 5.