The average number of cavities that thirty-year-old Americans have had in their lifetimes is 4. 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. 4, 3, 6, 6, 4, 3, 3, 3, 4, 5, 4, 4, 6, 3, 3 What can be concluded at the αα = 0.05 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: ? μ p Select an answer > < ≠ = H1:H1: ? p μ 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 fail to reject reject accept the null hypothesis. Thus, the final conclusion is that ... The data suggest the population mean is not significantly different from 4 at αα = 0.05, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is equal to 4. The data suggest that the population mean number of cavities for twenty-year-olds is not significantly different from 4 at αα = 0.05, so there is insufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is different from 4. The data suggest the populaton mean is significantly different from 4 at αα = 0.05, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is different from 4. Interpret the p-value in the context of the study. There is a 82.74993958% chance of a Type I error. There is a 82.74993958% chance that the population mean number of cavities for twenty-year-olds is not equal to 4. If the population mean number of cavities for twenty-year-olds is 4 and if you survey another 15 twenty-year-olds then there would be a 82.74993958% chance that the population mean would either be less than 3.93 or greater than 4. If the population mean number of cavities for twenty-year-olds is 4 and if you survey another 15 twenty-year-olds, then there would be a 82.74993958% chance that the sample mean for these 15 twenty-year-olds would either be less than 3.93 or greater than 4. Interpret the level of significance in the context of the study. There is a 5% chance that the population mean number of cavities for twenty-year-olds is different from 4. There is a 5% 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 4 and if you survey another 15 twenty-year-olds, then there would be a 5% chance that we would end up falsely concuding that the population mean number of cavities for twenty-year-olds is different from 4. If the population mean number of cavities for twenty-year-olds is different from 4 and if you survey another 15 twenty-year-olds, then there would be a 5% chance that we would end up falsely concuding that the population mean number of cavities for twenty-year-olds is equal to 4.

The average number of cavities that thirty-year-old Americans have had in their lifetimes is 4. 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. 4, 3, 6, 6, 4, 3, 3, 3, 4, 5, 4, 4, 6, 3, 3 What can be concluded at the αα = 0.05 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: ? μ p Select an answer > < ≠ = H1:H1: ? p μ 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 fail to reject reject accept the null hypothesis. Thus, the final conclusion is that ... The data suggest the population mean is not significantly different from 4 at αα = 0.05, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is equal to 4. The data suggest that the population mean number of cavities for twenty-year-olds is not significantly different from 4 at αα = 0.05, so there is insufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is different from 4. The data suggest the populaton mean is significantly different from 4 at αα = 0.05, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is different from 4. Interpret the p-value in the context of the study. There is a 82.74993958% chance of a Type I error. There is a 82.74993958% chance that the population mean number of cavities for twenty-year-olds is not equal to 4. If the population mean number of cavities for twenty-year-olds is 4 and if you survey another 15 twenty-year-olds then there would be a 82.74993958% chance that the population mean would either be less than 3.93 or greater than 4. If the population mean number of cavities for twenty-year-olds is 4 and if you survey another 15 twenty-year-olds, then there would be a 82.74993958% chance that the sample mean for these 15 twenty-year-olds would either be less than 3.93 or greater than 4. Interpret the level of significance in the context of the study. There is a 5% chance that the population mean number of cavities for twenty-year-olds is different from 4. There is a 5% 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 4 and if you survey another 15 twenty-year-olds, then there would be a 5% chance that we would end up falsely concuding that the population mean number of cavities for twenty-year-olds is different from 4. If the population mean number of cavities for twenty-year-olds is different from 4 and if you survey another 15 twenty-year-olds, then there would be a 5% chance that we would end up falsely concuding that the population mean number of cavities for twenty-year-olds is equal to 4.

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Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 22PFA

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4, 3, 6, 6, 4, 3, 3, 3, 4, 5, 4, 4, 6, 3, 3

What can be concluded at the αα = 0.05 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: ? μ p Select an answer > < ≠ =

H1:H1: ? p μ 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 fail to reject reject accept the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest the population mean is not significantly different from 4 at αα = 0.05, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is equal to 4.
- The data suggest that the population mean number of cavities for twenty-year-olds is not significantly different from 4 at αα = 0.05, so there is insufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is different from 4.
- The data suggest the populaton mean is significantly different from 4 at αα = 0.05, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is different from 4.
Interpret the p-value in the context of the study.
- There is a 82.74993958% chance of a Type I error.
- There is a 82.74993958% chance that the population mean number of cavities for twenty-year-olds is not equal to 4.
- If the population mean number of cavities for twenty-year-olds is 4 and if you survey another 15 twenty-year-olds then there would be a 82.74993958% chance that the population mean would either be less than 3.93 or greater than 4.
- If the population mean number of cavities for twenty-year-olds is 4 and if you survey another 15 twenty-year-olds, then there would be a 82.74993958% chance that the sample mean for these 15 twenty-year-olds would either be less than 3.93 or greater than 4.
Interpret the level of significance in the context of the study.
- There is a 5% chance that the population mean number of cavities for twenty-year-olds is different from 4.
- There is a 5% 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 4 and if you survey another 15 twenty-year-olds, then there would be a 5% chance that we would end up falsely concuding that the population mean number of cavities for twenty-year-olds is different from 4.
- If the population mean number of cavities for twenty-year-olds is different from 4 and if you survey another 15 twenty-year-olds, then there would be a 5% chance that we would end up falsely concuding that the population mean number of cavities for twenty-year-olds is equal to 4.

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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