For n = 25 independent observations from a normal population whose true mean u and true...

 

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For n = 25 independent observations from a normal population whose true mean u and true standard deviation o are both unknown: 1. How many degrees of freedom does the relevant Student's t distribution have? (1 point) 2. Construct a level C=95% confidence interval for the unknown meanu (2 points) 3. Compute (as numbers) the endpoints of the confidence interval if the sample mean is X25 = 3.65 and the sample standard deviation is $25 = 0.82 (1 point) 4. What can you say about the level of the confidence interval with margin m=0.25? (3 points) 5. How many extra observations will you need in order to construct a level 95% confidence interval with margin m=0.25? (3 points) 6. What formula will you use to construct your confidence interval, if you do get the necessary extra data? (1 point) For n = 25 independent observations from a normal population whose true mean u and true standard deviation o are both unknown: 1. How many degrees of freedom does the relevant Student's t distribution have? (1 point) 2. Construct a level C=95% confidence interval for the unknown meanu (2 points) 3. Compute (as numbers) the endpoints of the confidence interval if the sample mean is X25 = 3.65 and the sample standard deviation is $25 = 0.82 (1 point) 4. What can you say about the level of the confidence interval with margin m=0.25? (3 points) 5. How many extra observations will you need in order to construct a level 95% confidence interval with margin m=0.25? (3 points) 6. What formula will you use to construct your confidence interval, if you do get the necessary extra data? (1 point)

Answer rating: 100% (QA)

1 The relevant Students t distribution has n 1 degrees of freedom In this case n 25 so the degrees o... View the full answer