# Confidence Interval and Point Estimate Level of Confidence Discussion

### Question Description

I’m working on a statistics discussion question and need guidance to help me study.

1. Please go to the fish tutorial website (Links to an external site.) and follow the instructions for the tutorial. (The tutorial button is located in the lower middle of the screen.) Then answer the following questions:

- How did the applet visually show the confidence interval and the point estimate for the population mean?
- How did the applet visually show a confidence interval that did NOT capture the population mean? How often would we expect this to occur?
- What happened to the confidence intervals when the level of confidence increased to 99%?
- What happened to the confidence intervals when the sample size was increased to 40?

5. Did the applet help you understand what confidence intervals are? In your own words, what are confidence intervals?

__ðŸ’¦ __Write this first then give them reply from below posts. Do not use she,he, him ,her or this student. give them comment like your are giving them advice.A

**A.**

- How did the applet visually show the confidence interval and the point estimate for the population mean? It was shown by simulating random samples of fish.
- How did the applet visually show a confidence interval that did NOT capture the population mean? How often would we expect this to occur? The applet showed that the confidence level of 95% would be incorrect 5% of the time in estimating the true mean within the calculated upper and lower limits.
- What happened to the confidence intervals when the level of confidence increased to 99%? When the level of confidence increased, the intervals had to increase (become wider) which also demonstrates reduction in error to 1% in estimating the true mean.
- What happened to the confidence intervals when the sample size was increased to 40? When the sample size was increased, the the range of values grew narrower.

5. Did the applet help you understand what confidence intervals are? In your own words, what are confidence intervals? Yes, the applets help a lot! Confidence intervals are the estimate of the true mean showing up within the upper and lower limits you calculate for each scenario. So 95% confidence would have the true mean within the upper and lower limits 95% of the time and incorrect 5% of the time, and so on.

**B**.

- How did the applet visually show the confidence interval and the point estimate for the population mean?
- It took the mean(103 mm) marked it with a small orange box then put down the standard deviation (25.4mm(84.8 to 121.1))

- How did the applet visually show a confidence interval that did NOT capture the population mean? How often would we expect this to occur?
- It showed red. and added it to the failures above the numbers. I got 94.6% so 5.4% of the time?

- What happened to the confidence intervals when the level of confidence increased to 99%?
- It increases the standard deviation so less of them are outside.

- What happened to the confidence intervals when the sample size was increased to 40?
- The standard deviation decreased Narrowing the confidence interval.

- Did the applet help you understand what confidence intervals are? In your own words, what are confidence intervals?
- A confidence interval expresses our level of certainty about an estimate.
- A confidence interval is the accuracy.

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