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First identify the proper confidence interval. Since we are dealing with one proportion, a 1-proportion Z-interval is appropriate. Now check to see if the necessary conditions are fulfilled. First is whether the data was collected from a simple random sample representative of the population. Second is whether n * p-hat and n * (1 - p-hat) are both sufficiently large, where n is the sample size and p-hat is the sample proportion. This is the case, since both 135 and 500 - 135 = 365 are both greater than 10, a generally accepted value. Third is whether n is a sufficiently small fraction of the population (about 1/10 of the population is the largest acceptable fraction). If you have at least 5000 students in your population, the test can be used. Finally, the calculation (assuming all conditions have been fulfilled). The confidence interval for a proportion is p-hat +/- z-star * sqrt(p-hat * (1 - p-hat) / n). Here z-star is the critical value for which P(abs(Z) > z-star) on the standard normal curve is equal to 1 minus your confidence level. In this case, we're looking for the value where the probability of a standard normal random variable producing a value either greater than z-star or less than negative z-star is 1 - .95 = 0.05. This value is approximately 1.96. Putting it all together: p-hat = 135/500 = 0.27
z-star = 1.96
n = 500
0.27 +/- 1.96 * sqrt(0.27 * 0.73 / 500)
0.27 +/- 1.96 * sqrt(0.0003942)
0.27 +/- 1.96 * .0199
0.27 +/- .03891
We are 95% confident that the true proportion of students who own computers is between .23109 and .30891.

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โˆ™ 2007-05-16 02:20:23
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Q: If 135 out of 500 students sampled have computers what is the 95-percent confidence interval for the true proportion of all students who own computers?
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Related questions

What does a 95 percent confidence interval tell you about the population proportion?

There is a 95% probability that the true population proportion lies within the confidence interval.


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What is the most controllable method of increasing the precision of or narrowing the confidence interval?

Confidence intervals represent an interval that is likely, at some confidence level, to contain the true population parameter of interest. Confidence interval is always qualified by a particular confidence level, expressed as a percentage. The end points of the confidence interval can also be referred to as confidence limits.


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The confidence interval is not directly related to the mean.


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The confidence interval becomes smaller.


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Confidence intervals may be calculated for any statistics, but the most common statistics for which CI's are computed are mean, proportion and standard deviation. I have include a link, which contains a worked out example for the confidence interval of a mean.


Is confidence interval and confidence limits are same thing?

no,these are not the same thing.The values at each end of the interval are called the confidence limits.


What does a confidence interval for a population mean constructed from sample data show?

A confidence interval of x% is an interval such that there is an x% probability that the true population mean lies within the interval.


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The width of the confidence interval increases.


Is a 95 percent confidence interval for a mean wider than a 99 percent confidence interval?

No, it is not. A 99% confidence interval would be wider. Best regards, NS


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Generally speaking an x% confidence interval has a margin of error of (100-x)%.


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