SOLUTION: It is claimed that a random sample of 49 tyres has mean life of 15200 km. This sampled was drawn from a population whose mean is 15150 km's and a standard deviation of 1200 km. Tes
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Question 1205768: It is claimed that a random sample of 49 tyres has mean life of 15200 km. This sampled was drawn from a population whose mean is 15150 km's and a standard deviation of 1200 km. Test the significance at 0.05 level.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
sample size is 49.
sample mean is 15200.
population mean is 15150.
population standard deviation is 1200.
confidence interval is .95
standard error = standard deviation / sqrt(sample size) = 1200 / sqrt(49) = 171.4285714
z-score formula is z = (x-m)/s
z = the z-score
x = the sample mean
m = the population mean
s = the standard error
formula becomes:
z = (15200 - 15150) / 171.4285714 = .291666667.
area to the right of that z-score is equal to .3853.
this is much greater than the critical p-value of .05/2 = .025.
this indicates the results are not significant and that the sample mean is clearly within the confidence limits and therefore it is quite possible to get a sample mean of 15200 when the population mean is 15150.
here are the results using an online calculator with the population mean of 15150 and the standard error of 171.4285714.
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