The average number of cavities that thirty-year-old Americanshave had in their lifetimes is 5. Do twenty-year-olds have morecavities? The data show the results of a survey of 13twenty-year-olds who were asked how many cavities they have had.Assume that the distribution of the population is normal.

4, 7, 4, 6, 5, 4, 5, 5, 5, 5, 5, 4, 4

What can be concluded at the ?? = 0.01 level ofsignificance?

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

H0:H0:  ? ? p  ? = ? <>       

H1:H1:  ? p ?  ? = ? <>    

3. The test statistic ? z t  =  (please showyour answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimalplaces.)
5. The p-value is ? ? >  ??
6. Based on this, we should Select an answer fail to reject rejectaccept  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the population mean number of cavitiesfor twenty-year-olds is not significantly morethan 5 at ?? = 0.01, so there is insufficient evidence to concludethat the population mean number of cavities for twenty-year-olds ismore than 5.
   • The data suggest the population mean is notsignificantly more than 5 at ?? = 0.01, so thereis sufficient evidence to conclude that the population mean numberof cavities for twenty-year-olds is equal to 5.
   • The data suggest the populaton mean issignificantly more than 5 at ?? = 0.01, so thereis sufficient evidence to conclude that the population mean numberof cavities for twenty-year-olds is more than 5.
8. Interpret the p-value in the context of the study.
   • There is a 72.5686636% chance of a Type I error.
   • If the population mean number of cavities for twenty-year-oldsis 5 and if you survey another 13 twenty-year-olds then there wouldbe a 72.5686636% chance that the population mean number of cavitiesfor twenty-year-olds would be greater than 5.
   • If the population mean number of cavities for twenty-year-oldsis 5 and if you survey another 13 twenty-year-olds then there wouldbe a 72.5686636% chance that the sample mean for these 13twenty-year-olds would be greater than 4.85.
   • There is a 72.5686636% chance that the population mean numberof cavities for twenty-year-olds is greater than 5.
9. Interpret the level of significance in the context of thestudy.
   • If the population mean number of cavities for twenty-year-oldsis more than 5 and if you survey another 13 twenty-year-olds, thenthere would be a 1% chance that we would end up falsely concudingthat the population mean number of cavities for twenty-year-olds isequal to 5.
   • If the population mean number of cavities for twenty-year-oldsis 5 and if you survey another 13 twenty-year-olds, then therewould be a 1% chance that we would end up falsely concuding thatthe population mean number of cavities for twenty-year-olds is morethan 5.
   • There is a 1% chance that flossing will take care of theproblem, so this study is not necessary.
   • There is a 1% chance that the population mean number ofcavities for twenty-year-olds is more than 5.