Confidence Intervals (easy question)

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In summary, the conversation is about calculating a 95% confidence interval for the proportion of dies that pass the probe in semiconductor wafer testing. The question involves 365 dies, with 201 passing probing and a stable process assumption. The book's answer is .513 and .615, but the other person is not getting the same result and points out that the answer is not centered on the sample average. They also mention a possible typo in the formula for standard deviation and question if n is 356 or 365.
  • #1
Goalie_Ca
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Easy question but I'm being stupid somewhere. quite frustrating... enough to post it :surprise:

Basically the question is

Semiconductor wafer testing:
365 dies, 201 passed probing.
Assuming stable process calculate a 95% confidence interval for the proportion of all dies that pass the probe.

So x_bar = 201/365
std_dev = p*(1-p) = .228
n=356.

the answer in the book is .513,.615 and I'm not getting that. same for the next question and the one after lol.

:yuck: :yuck:
 
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  • #2
The answer you say is in the book can't be right because it is not centered on the sample average: 201/365= 0.551 ((.513+ .615)/2= .564). Also your formula for standard deviation is wrong: you need a squareroot. Although I suspect it is a typo, is n 356 or 365?
 
  • #3


I completely understand your frustration. Confidence intervals can be tricky, especially when it comes to calculating proportions. It's important to double check your calculations and make sure you're using the correct formula. In this case, the formula for calculating a confidence interval for a proportion is:

p +/- z*(√(p*(1-p)/n))

Where p is the proportion of successes, z is the z-score corresponding to the desired confidence level (in this case, 95% would correspond to a z-score of 1.96), and n is the sample size.

In your example, p = 201/365 = 0.551, z = 1.96, and n = 365. Plugging these values into the formula, we get:

0.551 +/- 1.96*(√(0.551*(1-0.551)/365)) = 0.551 +/- 0.032 = (0.519, 0.583)

So the confidence interval for the proportion of all dies that pass the probe is (0.519, 0.583). It's always a good idea to double check your calculations and make sure you're using the correct formula. Keep practicing and don't get discouraged, confidence intervals can be tricky but with practice, you'll become more confident in calculating them!
 

1. What is a confidence interval?

A confidence interval is a range of values that is likely to include the true population parameter with a certain degree of confidence. It is used to estimate the true value of a population parameter based on a sample of data.

2. How is a confidence interval calculated?

A confidence interval is calculated using the sample mean, standard deviation, and the desired level of confidence. The formula for a confidence interval is: CI = X ± Z * (σ/√n), where X is the sample mean, Z is the critical value from the standard normal distribution based on the desired level of confidence, σ is the standard deviation, and n is the sample size.

3. What is the difference between a confidence interval and a margin of error?

A confidence interval is a range of values that is likely to include the true population parameter, while a margin of error is the maximum amount that the sample estimate may differ from the true population parameter. The margin of error is often calculated as half the width of the confidence interval.

4. Why is it important to report a confidence interval?

Reporting a confidence interval allows for a more accurate interpretation of the data. It provides a range of values rather than a single point estimate and takes into account the variability in the data. This helps to avoid making false conclusions based on a single point estimate.

5. What factors can affect the width of a confidence interval?

The width of a confidence interval can be affected by the sample size, the level of confidence, and the variability in the data. A larger sample size, a higher level of confidence, and less variability in the data will result in a narrower confidence interval.

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