The average number of cavities that thirty-year-old Americans have had in their lifetimes is 4. Do twenty-year-olds have fewer 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.2, 3, 4, 3, 5, 5, 2, 3, 4, 2, 3, 4, 2, 2, 5, 5What can be concluded at the αα = 0.01 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 ααBased on this, we should the null hypothesis.Thus, the final conclusion is that ...The data suggest the populaton mean is significantly less than 4 at αα = 0.01, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is less than 4.The data suggest the population mean is not significantly less than 4 at αα = 0.01, 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 less than 4 at αα = 0.01, so there is insufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is less than 4.Interpret the p-value in the context of the study. There is a 2.77435624% chance of a Type I error.If the population mean number of cavities for twenty-year-olds is 4 and if you survey another 16 twenty-year-olds, then there would be a 2.77435624% chance that the population mean number of cavities for twenty-year-olds would be less than 4.There is a 2.77435624% chance that the population mean number of cavities for twenty-year-olds is less than 4.If the population mean number of cavities for twenty-year-olds is 4 and if you survey another 16 twenty-year-olds, then there would be a 2.77435624% chance that the sample mean for these 16 twenty-year-olds would be less than 3.38.Interpret the level of significance in the context of the study.There is a 1% chance that the population mean number of cavities for twenty-year-olds is less than 4.If the population mean number of cavities for twenty-year-olds is less than 4 and if you survey another 16 twenty-year-olds, then there would be a 1% chance that we would end up falsely concuding that the population mean number of cavities for twenty-year-olds is equal to 4.If the population mean number of cavities for twenty-year-olds is 4 and if you survey another 16 twenty-year-olds, then there would be a 1% chance that we would end up falsely concuding that the population mean number of cavities for twenty-year-olds is less than 4.There is a 1% chance that flossing will take care of the problem, so this study is not necessary.

Answered: Do twenty-year-olds have fewer…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

The average number of cavities that thirty-year-old Americans have had in their lifetimes is 4. Do twenty-year-olds have fewer 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.

2, 3, 4, 3, 5, 5, 2, 3, 4, 2, 3, 4, 2, 2, 5, 5

What can be concluded at the αα = 0.01 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 the populaton mean is significantly less than 4 at αα = 0.01, so there is sufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is less than 4.
- The data suggest the population mean is not significantly less than 4 at αα = 0.01, 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 less than 4 at αα = 0.01, so there is insufficient evidence to conclude that the population mean number of cavities for twenty-year-olds is less than 4.
Interpret the p-value in the context of the study.
- There is a 2.77435624% chance of a Type I error.
- If the population mean number of cavities for twenty-year-olds is 4 and if you survey another 16 twenty-year-olds, then there would be a 2.77435624% chance that the population mean number of cavities for twenty-year-olds would be less than 4.
- There is a 2.77435624% chance that the population mean number of cavities for twenty-year-olds is less than 4.
- If the population mean number of cavities for twenty-year-olds is 4 and if you survey another 16 twenty-year-olds, then there would be a 2.77435624% chance that the sample mean for these 16 twenty-year-olds would be less than 3.38.
- Interpret the level of significance in the context of the study.
  - There is a 1% chance that the population mean number of cavities for twenty-year-olds is less than 4.
  - If the population mean number of cavities for twenty-year-olds is less than 4 and if you survey another 16 twenty-year-olds, then there would be a 1% chance that we would end up falsely concuding that the population mean number of cavities for twenty-year-olds is equal to 4.
  - If the population mean number of cavities for twenty-year-olds is 4 and if you survey another 16 twenty-year-olds, then there would be a 1% chance that we would end up falsely concuding that the population mean number of cavities for twenty-year-olds is less than 4.
  - There is a 1% chance that flossing will take care of the problem, so this study is not necessary.

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 + ...

Expert Solution

Step 1

Given :

Claim : The population mean number of cavities for twenty-year-olds is less than 4.

Step by step

Solved in 5 steps with 2 images

SEE SOLUTION Check out a sample Q&A here