Question

The average number of cavities that thirty-year-old Americans have had in their lifetimes is 5. Do twenty-year-olds have a different number of cavities? The data show the results of a survey of 15 twenty-year-olds who were asked how many cavities they have had. Assume that the distribution of the population is normal.

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

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

H0:H0:  ? p μ  ? > ≠ < =       

H1:H1:  ? p μ  ? ≠ > < =    

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 ? > ≤  αα
6. Based on this, we should Select an answer accept reject fail to reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the population mean number of cavities for twenty-year-olds is not significantlydifferent from 5 at αα = 0.10, so there is insufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is different from 5.
   • The data suggest the population mean is not significantly different from 5 at αα = 0.10, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is equal to 5.
   • The data suggest the populaton mean is significantly different from 5 at αα = 0.10, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is different from 5.
8. Interpret the p-value in the context of the study.
   • There is a 1.91876214% chance that the population mean number of cavities for twenty-year-olds is not equal to 5.
   • If the population mean number of cavities for twenty-year-olds is 5 and if you survey another 15 twenty-year-olds, then there would be a 1.91876214% chance that the sample mean for these 15 twenty-year-olds would either be less than 4.33 or greater than 6.
   • There is a 1.91876214% chance of a Type I error.
   • If the population mean number of cavities for twenty-year-olds is 5 and if you survey another 15 twenty-year-olds then there would be a 1.91876214% chance that the population mean would either be less than 4.33 or greater than 6.
9. Interpret the level of significance in the context of the study.
   • If the population mean number of cavities for twenty-year-olds is 5 and if you survey another 15 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 different from 5.
   • There is a 10% chance that the population mean number of cavities for twenty-year-olds is different from 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 different from 5 and if you survey another 15 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.

Answer 1

Note: please check the p-value with your professor, maybe he used a different tool but it should be same. It might be a misprint.