The average number of cavities that 30-year-old Americans have had in their lifetimes is 7.0. The standard deviation 2.7 cavities. Is the mean different for 20-year-olds? The data show the results of a survey of 15 twenty-year-olds who were asked how many cavities they have had. Assume that that distribution of the population is normal. 6, 7, 5, 3, 7, 8, 4, 6, 5, 6, 4, 6, 7, 6, 9 What can be concluded at the 0.05 level of significance? H0: = 7 Ha: [ Select ] ["<", ">", "Not Equal To"] 7 Test statistic: [ Select ] ["Z", "T"] p-Value = [ Select ] ["0.13", "0.26", "0.03", "0.06"] [ Select ] ["Fail to Reject Ho", "Reject Ho"] Conclusion: There is [ Select ] ["statistically insignificant", "statistically significant"] evidence to make the conclusion that the population mean number of cavities for 20-year-olds differs from 7.0. p-Value Interpretation: If the mean number of cavities for 20-year-olds is equal to [ Select ] ["7", "13", "6", "3", "5.9"] and if another study was done with a new randomly selected group of 15 twenty-year-olds, then there is a [ Select ] ["6", "7", "5", "13"] percent chance that the mean number of cavities for this new sample would be less than [ Select ] ["3.4", "6", "5.9", "7"] or greater than [ Select ] ["7.9", "8.4", "8.1", "7.7"] . Level of significance interpretation: If the mean number cavities for twenty-year-olds is equal to [ Select ] ["7", "13", "5.9", "6"] and if many studies are done with with a group of 15 randomly selected 20-year-olds each then [ Select ] ["50", "5", "5.9", "10"] percent of these studies would result in the false conclusion that the mean number of cavities per person for 20-year-olds is not equal to 7.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
27.
The average number of cavities that 30-year-old Americans have had in their lifetimes is 7.0. The standard deviation 2.7 cavities. Is the mean different for 20-year-olds? The data show the results of a survey of 15 twenty-year-olds who were asked how many cavities they have had. Assume that that distribution of the population is normal.
6, 7, 5, 3, 7, 8, 4, 6, 5, 6, 4, 6, 7, 6, 9
What can be concluded at the 0.05 level of significance?
H0: = 7
Ha: [ Select ] ["<", ">", "Not Equal To"] 7
Test statistic: [ Select ] ["Z", "T"]
p-Value = [ Select ] ["0.13", "0.26", "0.03", "0.06"]
[ Select ] ["Fail to Reject Ho", "Reject Ho"]
Conclusion: There is [ Select ] ["statistically insignificant", "statistically significant"] evidence to make the conclusion that the population mean number of cavities for 20-year-olds differs from 7.0.
p-Value Interpretation: If the mean number of cavities for 20-year-olds is equal to [ Select ] ["7", "13", "6", "3", "5.9"] and if another study was done with a new randomly selected group of 15 twenty-year-olds, then there is a [ Select ] ["6", "7", "5", "13"] percent chance that the mean number of cavities for this new sample would be less than [ Select ] ["3.4", "6", "5.9", "7"] or greater than [ Select ] ["7.9", "8.4", "8.1", "7.7"] .
Level of significance interpretation: If the mean number cavities for twenty-year-olds is equal to [ Select ] ["7", "13", "5.9", "6"] and if many studies are done with with a group of 15 randomly selected 20-year-olds each then [ Select ] ["50", "5", "5.9", "10"] percent of these studies would result in the false conclusion that the mean number of cavities per person for 20-year-olds is not equal to 7.
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