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 16 twenty-year-olds who were asked how many cavities they have had. Assume that the distribution of the population is normal.

8, 5, 5, 6, 5, 11, 9, 7, 10, 6, 9, 7, 6, 6, 11, 10

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

For this study, we should use Select an answer z-test for a population proportion t-test for a population mean

The null and alternative hypotheses would be:

H0:H0:  ? p μ  Select an answer = ≠ > <

H1:H1:  ? μ p  Select an answer > ≠ < =

The test statistic ? t z  =  (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 Select an answer reject accept fail to reject  the null hypothesis.

Thus, the final conclusion is that ...

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 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 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 1.77274508% chance that the population mean number of cavities for twenty-year-olds is not equal to 9.

There is a 1.77274508% chance of a Type I error.

If the population mean number of cavities for twenty-year-olds is 9 and if you survey another 16 twenty-year-olds then there would be a 1.77274508% chance that the population mean would either be less than 7.56 or greater than 10.44.

If the population mean number of cavities for twenty-year-olds is 9 and if you survey another 16 twenty-year-olds, then there would be a 1.77274508% chance that the sample mean for these 16 twenty-year-olds would either be less than 7.56 or greater than 10.44.

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.

If the population mean number of cavities for twenty-year-olds is different from 9 and if you survey another 16 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.

If the population mean number of cavities for twenty-year-olds is 9 and if you survey another 16 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.

There is a 10% chance that the population mean number of cavities for twenty-year-olds is different from 9.

Name: The average number of cavities that thirty-year-old Americans have had
Uploaded: 2024-03-20T07:07:12.000Z
Channel: Bartleby
Description: 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 16 twenty-year-olds who were asked how many cavities th

Question

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 16 twenty-year-olds who were asked how many cavities they have had. Assume that the distribution of the population is normal.

8, 5, 5, 6, 5, 11, 9, 7, 10, 6, 9, 7, 6, 6, 11, 10

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

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

H0:H0: ? p μ Select an answer = ≠ > <

H1:H1: ? μ p Select an answer > ≠ < =

The test statistic ? t z = (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 Select an answer reject accept fail to reject the null hypothesis.
Thus, the final conclusion is that ...
- 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 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 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 1.77274508% chance that the population mean number of cavities for twenty-year-olds is not equal to 9.
- There is a 1.77274508% chance of a Type I error.
- If the population mean number of cavities for twenty-year-olds is 9 and if you survey another 16 twenty-year-olds then there would be a 1.77274508% chance that the population mean would either be less than 7.56 or greater than 10.44.
- If the population mean number of cavities for twenty-year-olds is 9 and if you survey another 16 twenty-year-olds, then there would be a 1.77274508% chance that the sample mean for these 16 twenty-year-olds would either be less than 7.56 or greater than 10.44.
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.
- If the population mean number of cavities for twenty-year-olds is different from 9 and if you survey another 16 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.
- If the population mean number of cavities for twenty-year-olds is 9 and if you survey another 16 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.
- There is a 10% chance that the population mean number of cavities for twenty-year-olds is different from 9.

Accepted Answer

Given data:
8,5,5,6,5,11,9,7,10,6,9,7,6,6,11,10
Sample Mean, x̄ = Σx/n = 121/16 = 7.5625
Variance,…