As you increased the variance, what happened to the proportion of confidence int

Question

As you increased the variance, what happened to the proportion of confidence intervals that captured the true population mean? Question 3b. As you increased the variance, what happened to the width of the confidence intervals? Did they get wider, narrower, or did they stay the same size? (Hint: Look at the numbers on the x-axis closely when you change these!). Question 3c. Based on your answer in question 3b, does this make estimates for the mean in each sample more precise, less precise, or the same level of precision as the variance increases?

Explanation / Answer

As you increased the variance, what happened to the proportion of confidence intervals that captured the true population mean?

Upon increase the variance, the proportion of confidence intervals that captured the true population mean INCREASES

Question 3b. As you increased the variance, what happened to the width of the confidence intervals?

INCREASES, it became wider

Did they get wider, narrower, or did they stay the same size?

Question 3c. Based on your answer in question 3b, does this make estimates for the mean in each sample more precise, less precise, or the same level of precision as the variance increases?

It becomes less precise. If you're comparing confidence intervals for the same sort of parameter from multiple data sets and one is smaller than the other, you could say that the smaller one is more precise. I prefer to talk about precision rather than accuracy in this situation

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