SOLUTION: a manufacturer claims that the amount of peanuts contained in a jar follows normal distribution with the mean 7 ounces.A quality control inspector,however disagrees and believes it

Question 259974: a manufacturer claims that the amount of peanuts contained in a jar follows normal distribution with the mean 7 ounces.A quality control inspector,however disagrees and believes it is some value below this figure.In order to test this belief the inspector takes random variable 25 jars and finds that the sample mean is 6.5 and sample standard deviation 0.9 ounces.
- what is probability of sample mean smaller than 6.5
-what are the null and alternative hypothesis inspector should test?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
a manufacturer claims that the amount of peanuts contained in a jar follows normal distribution with the mean 7 ounces.A quality control inspector,however disagrees and believes it is some value below this figure.In order to test this belief the inspector takes random variable 25 jars and finds that the sample mean is 6.5 and sample standard deviation 0.9 ounces.
- what is probability of sample mean smaller than 6.5
t(6.5) = (6.5-7)/0.9 = -0.56
P(x<6.5) = P(t<-0.56 when df = 24) = tcdf(-100,-0.56,24) = 0.2903
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-what are the null and alternative hypothesis inspector should test?
--------------------
Ho: u = 7
Ha: u < 7
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Cheers,
Stan H.
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