A market analyst is estimating the average monthly spending on online subscriptions among young adults. The point estimate y for the average monthly spending is $ 45.60 \$45.60 , with a margin of error E E of $ 3.20 \$3.20 at a 90 % 90\% confidence level. Write and interpret a 90 % 90\% Confidence Interval for the average monthly spending.

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 of 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.

7. Sampling Distributions & Confidence Intervals: Mean

Introduction to Confidence Intervals

Statistics for Business

7. Sampling Distributions & Confidence Intervals: Mean

Introduction to Confidence Intervals

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Multiple Choice

A market analyst is estimating the average monthly spending on online subscriptions among young adults. The point estimate y for the average monthly spending is $dollar sign 45.60$ , with a margin of error $E$ of $dollar sign 3.20$ at a $90 percent sign$ confidence level. Write and interpret a $90 percent sign$ Confidence Interval for the average monthly spending.

($44.00, $47.2); We are 90% confident that ($44.00, $47.2) contains the true average monthly spending.

($42.72, $48.48); We are 90% confident that ($42.72, $48.48) contains the true average monthly spending.

($45.28, $45.92); We are 90% confident that ($45.28, $45.92) contains the true average monthly spending.

($42.40, $48.40); We are 90% confident that ($42.40, $48.40) contains the true average monthly spending.

Verified step by step guidance

Identify the point estimate for the average monthly spending, which is given as $45.60.

Recognize the margin of error provided, which is $3.20.

Understand that a confidence interval is calculated as the point estimate plus or minus the margin of error.

Calculate the lower bound of the confidence interval by subtracting the margin of error from the point estimate: $45.60 - $3.20.

Calculate the upper bound of the confidence interval by adding the margin of error to the point estimate: $45.60 + $3.20.

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