We want to make an hypothesis test for the mean value &#x03BC;<!-- μ --> of a normal populatio

deformere692qr 2022-05-09 Answered
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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Answers (1)

Lea Johnson
Answered 2022-05-10 Author has 10 answers
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)
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