8.10. PA Nationally, the per capita monthly fuel oil bill is $110. A random sample of 36 cities in the Southeast average $78, with a standard deviation of s4. Is the difference significant? Summarize your conclusions in a sentence or two.
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.
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08 Additional Problems: Hypothesis Testing I: The One-Sample Case
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8.10. PA Nationally, the per capita monthly fuel oil bill is $110. A random sample of 36 cities in the
Southeast average $78, with a standard deviation of $4. Is the difference significant? Summarize your
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conclusions in a sentence or two.
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8.11. GER/CJ A survey shows that 10% of the population is victimized by property crime each year. A
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random sample of 527 older citizens (65 years or more of age) shows a victimization rate of 14%. Are
older people more likely to be victimized? Conduct both one- and two-tailed tests of significance.
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Answer +
8.12. CJ A random sample of 113 felons convicted of nonviolent crimes in a state prison system completed a
program designed to improve their employment possibilities before being released on parole. Fifty-eight
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eventually became repeat offenders. Is this recidivism rate significantly different from the rate for all
offenders in that state (57%)? Summarize your conclusions in a sentence or two. (HINT: You must use the
information given in the problem to compute a sample proportion. Remember to convert the population
percentage to a proportion.)
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8.13. PS In a recent statewide election, 55% of the voters rejected a proposal to institute a state lottery. In a
random sample of 150 urban precincts, 49% of the voters rejected the proposal. Is the difference
significant? Summarize your conclusions in a sentence or two.
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