The average number of cavities that thirty-year-old Americans have had in their lifetimes is 9. 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.8, 5, 10, 5, 10, 10, 8, 7, 7, 5, 9, 7, 11What can be concluded at the αα = 0.10 level of significance?For this study, we should use (t-test for population mean, z-test for population proportion)The null and alternative hypotheses would be: H0: (symbol) (symbol) ____ H1: (symbol) (symbol) ___ The test statistic (?,z,t) = _____ (please show your answer to 3 decimal places.)The p-value = _____ (Please show your answer to 4 decimal places.)The p-value is (?, less than or equal to, more than) ααBased on this, we should (accept, reject, fail to reject) the null hypothesis.Thus, the final conclusion is that ...The data suggest the population mean is not significantly different from 9 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 9.The data suggest the populaton mean is significantly different from 9 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 9.The data suggest that the population mean number of cavities for twenty-year-olds is not significantly different from 9 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 9.Interpret the p-value in the context of the study.There is a 6.8119839% chance that the population mean number of cavities for twenty-year-olds is not equal to 9.If the population mean number of cavities for twenty-year-olds is 9 and if you survey another 13 twenty-year-olds then there would be a 6.8119839% chance that the population mean would either be less than 7.85 or greater than 10.15.If the population mean number of cavities for twenty-year-olds is 9 and if you survey another 13 twenty-year-olds, then there would be a 6.8119839% chance that the sample mean for these 13 twenty-year-olds would either be less than 7.85 or greater than 10.15.There is a 6.8119839% chance of a Type I error.Interpret the level of significance in the context of the study.There is a 10% chance that flossing will take care of the problem, so this study is not necessary.There is a 10% chance that the population mean number of cavities for twenty-year-olds is different from 9.If the population mean number of cavities for twenty-year-olds is 9 and if you survey another 13 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 9.If the population mean number of cavities for twenty-year-olds is different from 9 and if you survey another 13 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 9.

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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The average number of cavities that thirty-year-old Americans have had in their lifetimes is 9. 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.

8, 5, 10, 5, 10, 10, 8, 7, 7, 5, 9, 7, 11

What can be concluded at the αα = 0.10 level of significance?

For this study, we should use (t-test for population mean, z-test for population proportion)
The null and alternative hypotheses would be:

H0: (symbol) (symbol) ____

H1: (symbol) (symbol) ___

The test statistic (?,z,t) = _____ (please show your answer to 3 decimal places.)
The p-value = _____ (Please show your answer to 4 decimal places.)
The p-value is (?, less than or equal to, more than) αα
Based on this, we should (accept, reject, fail to reject) the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest the population mean is not significantly different from 9 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 9.
- The data suggest the populaton mean is significantly different from 9 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 9.
- The data suggest that the population mean number of cavities for twenty-year-olds is not significantly different from 9 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 9.
Interpret the p-value in the context of the study.
- There is a 6.8119839% chance that the population mean number of cavities for twenty-year-olds is not equal to 9.
- If the population mean number of cavities for twenty-year-olds is 9 and if you survey another 13 twenty-year-olds then there would be a 6.8119839% chance that the population mean would either be less than 7.85 or greater than 10.15.
- If the population mean number of cavities for twenty-year-olds is 9 and if you survey another 13 twenty-year-olds, then there would be a 6.8119839% chance that the sample mean for these 13 twenty-year-olds would either be less than 7.85 or greater than 10.15.
- There is a 6.8119839% chance of a Type I error.
Interpret the level of significance in the context of the study.
- There is a 10% chance that flossing will take care of the problem, so this study is not necessary.
- There is a 10% chance that the population mean number of cavities for twenty-year-olds is different from 9.
- If the population mean number of cavities for twenty-year-olds is 9 and if you survey another 13 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 9.
- If the population mean number of cavities for twenty-year-olds is different from 9 and if you survey another 13 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 9.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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