Do twenty-year-olds have fewer cavities? The data show the results of a survey of 16 twenty-year-olds who were asked how many cavities they have had. Assume that the distribution of the population is normal. 2, 3, 4, 3, 5, 5, 2, 3, 4, 2, 3, 4, 2, 2, 5, 5 What can be concluded at the αα

The average number of cavities that thirty-year-old Americans have had in their lifetimes is 4.  Do twenty-year-olds have fewer cavities? The data show the results of a survey of 16 twenty-year-olds who were asked how many cavities they have had. Assume that the distribution of the population is normal.

2, 3, 4, 3, 5, 5, 2, 3, 4, 2, 3, 4, 2, 2, 5, 5

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

1. For this study, we should use    
2. The null and alternative hypotheses would be:     

 H0:H0:                 

 H1:H1:              

1. The test statistic     =  (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     αα
4. Based on this, we should      the null hypothesis.
5. Thus, the final conclusion is that ...
   • The data suggest the populaton mean is significantly less than 4 at αα = 0.01, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is less than 4.
   • The data suggest the population mean is not significantly less than 4 at αα = 0.01, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is equal to 4.
   • The data suggest that the population mean number of cavities for twenty-year-olds is not significantly less than 4 at αα = 0.01, so there is insufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is less than 4.
6. Interpret the p-value in the context of the study.
   •  There is a 2.77435624% chance of a Type I error.
   • If the population mean number of cavities for twenty-year-olds is 4 and if you survey another 16 twenty-year-olds, then there would be a 2.77435624% chance that the population mean number of cavities for twenty-year-olds would be less than 4.
   • There is a 2.77435624% chance that the population mean number of cavities for twenty-year-olds is less than 4.
   • If the population mean number of cavities for twenty-year-olds is 4 and if you survey another 16 twenty-year-olds, then there would be a 2.77435624% chance that the sample mean for these 16 twenty-year-olds would be less than 3.38.
   • 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 less than 4.
     • If the population mean number of cavities for twenty-year-olds is less than 4 and if you survey another 16 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 4.
     • If the population mean number of cavities for twenty-year-olds is 4 and if you survey another 16 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 less than 4.
     • There is a 1% chance that flossing will take care of the problem, so this study is not necessary.
   •