Make a 90% confidence interval for a parameter, y, with point estimate y ^ = − 1.5 ŷ=-1.5 y ^ = − 1.5 , & margin of error E = 3.25 E=3.25 E = 3.25 .

Here, we're asked to make a 90% confidence interval for a parameter y with a point estimate y hat of negative 1.5 and a margin of error e of 3.25. Now because here we're explicitly given our point estimate and our margin of error, we can easily figure out what the endpoints of our confidence interval are. So one of my endpoints is going to be a y hat minus that margin of error e, and the other is going to be a y hat, my point estimate, plus my margin of error e. So actually just plugging in these values, this will give me negative 1.5 minus 3.25 and negative 1.5 plus 3.25. So this thing gives me endpoints here of negative 4.75 and positive 1.75. Now another way that we could choose to write this is just an interval notation as negative 4.75 comma, 1.75. Or we could write this in its most compact form, which would be negative 1.5 plus or minus 3.25. But it is often more useful to actually come up with what those endpoints are. Now a really important part of confidence intervals is knowing how to interpret what they actually mean once you find your endpoints and you have your confidence level. So if you haven't already, think about what this means in the context of this problem. Now looking at this interval from negative 4.75 to 1.75 and my confidence level of 90%, I can interpret everything that's going on here by saying that we are 90% confident that our parameter y is in between negative 4.75 and positive 1.75. So that's what's actually going on here. Feel free to let us know if you have any questions, and I'll see you in the next one.

Make a 90% confidence interval for a parameter, y, with point est...

7. Sampling Distributions & Confidence Intervals: Mean

Introduction to Confidence Intervals

Statistics

7. Sampling Distributions & Confidence Intervals: Mean

Introduction to Confidence Intervals

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Multiple Choice

Make a 90% confidence interval for a parameter, y, with point estimate $ŷ=-1.5$ , & margin of error $E=3.25$ .

(-1.5, 3.25)

(1.75, 4.75)

(-3.25, -1.5)

(-4.75, 1.75)

Verified step by step guidance

Identify the point estimate and the margin of error from the problem. The point estimate is given as $ \hat{y} = -1.5 $ and the margin of error is $ E = 3.25 $.

Understand that a confidence interval is calculated using the formula: $ \text{Confidence Interval} = (\hat{y} - E, \hat{y} + E) $.

Substitute the given values into the confidence interval formula. This means you will calculate $ (-1.5 - 3.25, -1.5 + 3.25) $.

Perform the subtraction for the lower bound: $ -1.5 - 3.25 $.

Perform the addition for the upper bound: $ -1.5 + 3.25 $.

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Make a 90% confidence interval for a parameter, y, with point estimate y^=−1.5ŷ=-1.5y^=−1.5, & margin of error E=3.25E=3.25E=3.25.

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Make a 90% confidence interval for a parameter, y, with point estimate $ŷ=-1.5$ , & margin of error $E=3.25$ .