The average number of cavities that thirty-year-old Americans have had in their lifetimes is 7. Do twenty-year-olds have a different number of cavities? The data show the results of a survey of 13...

The average number of cavities that thirty-year-old Americans have had in their lifetimes is 7.  Do twenty-year-olds have a different number of 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.

9, 8, 8, 10, 10, 9, 9, 10, 6, 6, 9, 8, 8

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

1. Thus, the final conclusion is that ...
   
   
   

   
   
   • The data suggest the population mean is notsignificantly different from 7 at α = 0.01, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is equal to 7.
   
   
   • The data suggest that the population mean number of cavities for twenty-year-olds is notsignificantly different from 7 at α = 0.01, so there is insufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is different from 7.
   
   
   • The data suggest the populaton mean issignificantly different from 7 at α = 0.01, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is different from 7.
   
   

   
   
   
   


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

   
   
   • If the population mean number of cavities for twenty-year-olds is 7 and if you survey another 13 twenty-year-olds, then there would be a 0.18872783999999% chance that the sample mean for these 13 twenty-year-olds would either be less than 5.54 or greater than 8.
   
   
   • If the population mean number of cavities for twenty-year-olds is 7 and if you survey another 13 twenty-year-olds then there would be a 0.18872783999999% chance that the population mean would either be less than 5.54 or greater than 8.
   
   
   • There is a 0.18872783999999% chance that the population mean number of cavities for twenty-year-olds is not equal to 7.
   
   
   • There is a 0.18872783999999% chance of a Type I error.
   
   

   
   
   
   


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

   
   
   • There is a 1% chance that flossing will take care of the problem, so this study is not necessary.
   
   
   • There is a 1% chance that the population mean number of cavities for twenty-year-olds is different from 7.
   
   
   • If the population mean number of cavities for twenty-year-olds is 7 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 different from 7.
   
   
   • If the population mean number of cavities for twenty-year-olds is different from 7 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 7.