Question

1 Joe computed a 95% confidence interval for µ from a specific random sample. His confidence interval was 10.1<µ<12.2. He claims that the probability   that µ is in this interval 0.95. What is wrong with his claim? Explain.

2. Consider a test for µ. If the P-value is such that you can reject H0 for α=0.01, can you always reject H0 for α =0.05? Explain.

PLZ PLZ help me with 1 and 2 and plz write in your own words in text not in pic since its hard to read from a pic thank you

Answer 1

1. A confidence interval does not enable us to make statements about probability. If we say that confidence interval for the population parameter is 10.1<µ<12.2, it means that we can say with 95% confidence that the population parameter lies within this interval. Confidence is not the same as probability. Claiming that the probability of lying in this interval is wrong.

2. In order to reject H0 for α=0.01, that would mean that the p-value < 0.01, then only we would be able to reject H0 at 0.01 level of significance. This would further imply that we would be able to reject H0 at 0.05 always. This is since p-value < 0.01, it is definitely <0.05

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