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. 13, 12, 8, 7, 10, 9, 9, 12, 12, 13, 12, 9, 8 What can be concluded at the a = 0.10 level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: Họ: P V= 9 c. The test statistic t V= 2.248 (please show your answer to 3 decimal places.) d. The p-value = 0.0442 (Please show your answer to 4 decimal places.) e. The p-value is ? Va f. Based on this, we should Select an answer V the null hypothesis. g. Thus, the final conclusion is that ... O The data suggest the population mean is not significantly different from 9 at a = 0.10o, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is equal to 9. O The data suggest that the population mean number of cavities for twenty-year-olds is not significantly different from 9 at a = 0.10, so there is insufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is different from 9. O The data suggest the populaton mean is significantly different from 9 at a = 0.10, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year- olds is different from 9. h. Interpret the p-value in the context of the study. O There is a 4.41226428% chance of a Type I error. OIf 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 4.41226428% chance that the sample mean for these 13 twenty-year-olds would either be less than 7.69 or greater than 10. O There is a 4.41226428% chance that the population mean number of cavities for twenty-year- olds is not equal to 9. OIf 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 4.41226428% chance that the population mean would either be less than 7.69 or greater than 10. i. Interpret the level of significance in the context of the study. O There is a 10% chance that flossing will take care of the problem, so this study is not necessary. Olf 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. O There is a 10% chance that the population mean number of cavities for twenty-year-olds is different from 9. OIf 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.

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i already have answer in question A-D. please help me to solve the rest. topic is unkown standard deviation

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.
13, 12, 8, 7, 10, 9, 9, 12, 12, 13, 12, 9, 8
What can be concluded at the a = 0.10 level of significance?
a. For this study, we should use t-test for a population mean
b. The null and alternative hypotheses would be:
Ho: H V=
9
H1: P V#
9
c. The test statistic t V=
2.248
(please show your answer to 3 decimal places.)
d. The p-value = 0.0442
(Please show your answer to 4 decimal places.)
e. The p-value is ? Va
f. Based on this, we should Select an answer v the null hypothesis.
g. Thus, the final conclusion is that ...
O The data suggest the population mean is not significantly different from 9 at a = 0.10, so
there is sufficient evidence to conclude that the population mean number of cavities for
twenty-year-olds is equal to 9.
O The data suggest that the population mean number of cavities for twenty-year-olds is not
significantly different from 9 at a = 0.10, so there is insufficient evidence to conclude that
the population mean number of cavities for twenty-year-olds is different from 9.
O The data suggest the populaton mean is significantly different from 9 at a = 0.10, so there is
sufficient evidence to conclude that the population mean number of cavities for twenty-year-
olds is different from 9.
h. Interpret the p-value in the context of the study.
O There is a 4.41226428% chance of a Type I error.
O 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 4.41226428% chance that the sample mean for
these 13 twenty-year-olds would either be less than 7.69 or greater than 10.
O There is a 4.41226428% chance that the population mean number of cavities for twenty-year-
olds is not equal to 9.
O f 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 4.41226428% chance that the population mean
would either be less than 7.69 or greater than 10.
i. Interpret the level of significance in the context of the study.
O There is a 10% chance that flossing will take care of the problem, so this study is not
necessary.
O 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.
O There is a 10% chance that the population mean number of cavities for twenty-year-olds is
different from 9.
OIf 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.
Transcribed Image Text: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. 13, 12, 8, 7, 10, 9, 9, 12, 12, 13, 12, 9, 8 What can be concluded at the a = 0.10 level of significance? a. For this study, we should use t-test for a population mean b. The null and alternative hypotheses would be: Ho: H V= 9 H1: P V# 9 c. The test statistic t V= 2.248 (please show your answer to 3 decimal places.) d. The p-value = 0.0442 (Please show your answer to 4 decimal places.) e. The p-value is ? Va f. Based on this, we should Select an answer v the null hypothesis. g. Thus, the final conclusion is that ... O The data suggest the population mean is not significantly different from 9 at a = 0.10, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is equal to 9. O The data suggest that the population mean number of cavities for twenty-year-olds is not significantly different from 9 at a = 0.10, so there is insufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is different from 9. O The data suggest the populaton mean is significantly different from 9 at a = 0.10, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year- olds is different from 9. h. Interpret the p-value in the context of the study. O There is a 4.41226428% chance of a Type I error. O 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 4.41226428% chance that the sample mean for these 13 twenty-year-olds would either be less than 7.69 or greater than 10. O There is a 4.41226428% chance that the population mean number of cavities for twenty-year- olds is not equal to 9. O f 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 4.41226428% chance that the population mean would either be less than 7.69 or greater than 10. i. Interpret the level of significance in the context of the study. O There is a 10% chance that flossing will take care of the problem, so this study is not necessary. O 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. O There is a 10% chance that the population mean number of cavities for twenty-year-olds is different from 9. OIf 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.
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