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According to the rules established for a mechanical aptitude test, 18-year-olds must average 73.2 with a...

According to the rules established for a mechanical aptitude test, 18-year-olds must average 73.2 with a standard deviation of 8.6. 45 people of that age are chosen at random, averaging 76.7.
a) Find the critical value to use if a significance level of α = 0.01 will be used and it is a right tail test
b) How many standard deviations is the sample mean of the presumed population mean?
c) Test the hypothesis that the average has improved. H0: µ <= 73.2, HA: µ> 73.2 with a significance level of α = 0.01.

Math   Statistics-And-Probability   
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