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):
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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.