We want to make an hypothesis test for the mean value μ of a normal population with known variance σ 2 = 13456, using a sample of size n = 100 that has sample mean value equal to 562.Calculate the p-value.Make the test with significance level 1 % about if the population mean value from which the sample comes from is greater than 530 using the p-value.For the first one, about the p-value, do we have to calculate P ( 530 − 562 σ n ) ?And for the second we have to check the p-value with the significance level, right?

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We want to make an hypothesis test for the mean value   μ of a normal population with known variance       σ    2    =  13456, using a sample of size   n  =  100 that has sample mean value equal to   562.Calculate the   p-value.Make the test with significance level   1  % about if the population mean value from which the sample comes from is greater than   530 using the   p-value.For the first one, about the   p-value, do we have to calculate   P      (                  530        −        562                    σ                  n                      )  ?And for the second we have to check the   p-value with the significance level, right?

Lea Johnson · Accepted Answer

Yes. correct.If you calculate   Φ  (            530      −      562              134.56        )  =  Φ  (  −  2.76  )  ≈  0.29  %this   p-value is highly significant so the test is significant at   1  % and the hypothesis that the mean is   530 is rejected.Lower is the   p-value and higher is the significance of the test. This because the p-value is the area of the queue. A very low value of   p indicates that the quantile (your observed mean) is very far from the centered mean (null hypothesis)

We want to make an hypothesis test for the mean value μ of a normal populatio

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