Question 1032697: . The director of manufacturing of a toy company is investigating vendors who supply handheld gyroscopes for inclusion into one of their most recent product lines. The director would like to estimate the diameter of gyroscopes that are currently used in the toy line to determine if they still comply with product specifications. The principal manufacturing vendor has specified that the gyros are supposed to have a population mean diameter of 7.30 inches and a standard deviation equal to .04 inches. A random sample of 25 selected from a shipment indicates a sample average of 7.31 inches. Set up a 95% confidence interval estimate of the true average diameter of the gyroscopes in this shipment. Does the population of gyros need to have a diameter that is normally distributed here?
Thank you!!
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Assumptions have to be a normally distributed population where the population variance is estimated by the sample's variance. One could try using the central limit theorem to say that as the sample size increases, the sample tends towards normality, but 25 is not a large sample in the absence of any other information.
Ho=mean is 7.30
Ha=mean is not 7.30
alpha=0.05 P {reject Ho|Ho true}
test stat is a t df=24
critical value |t|>2.064
calculation t=(7.31-7.30)/s/ sqrt(n)
that is 0.01*5/0.04=1.25
Fail to reject Ho
95% CI is 2.064*0.04/5 on either side=0.0165
(7.294,7.327) Since the CI contains the hypothesized value of the parameter, fail to reject Ho
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