MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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 αα = 0.10 level of significance?
- For this study, we should use
- The null and alternative hypotheses would be:
H0:H0:
H1:H1:
- The test statistic = (please show your answer to 3 decimal places.)
- The p-value = (Please show your answer to 4 decimal places.)
- The p-value is αα
- Based on this, we should the null hypothesis.
- Thus, the final conclusion is that ...
- The data suggest that the population
mean number of cavities for twenty-year-olds is not significantly less than 5 at αα = 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 αα = 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 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 that the population
- Interpret the p-value in the context of the study.
- 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.
- 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.
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