How To Find A Confidence Interval On Ti 84

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How To Find A Confidence Interval On Ti 84

How to Find a Confidence Interval on a TI-84 Calculator

In statistics, a confidence interval is a range of values that is likely to contain the true value of a parameter. Confidence intervals are used to estimate the population mean, proportion, or standard deviation. In this article, we will show you how to find a confidence interval on a TI-84 calculator.

Before we begin, we need to define some terms. A population is a group of all individuals or objects that we are interested in studying. A sample is a subset of the population that we actually observe. The population mean is the average value of the population. The sample mean is the average value of the sample. The standard deviation is a measure of how spread out the data is. The confidence level is the probability that the confidence interval will contain the true value of the parameter.

Finding a Confidence Interval for a Mean

To find a confidence interval for a mean, we need to know the following information:

  • The sample mean
  • The sample standard deviation
  • The sample size
  • The confidence level

Once we have this information, we can use the following formula to find the confidence interval:

CI = x̄ ± Z * (s / √n)

where:

  • CI is the confidence interval
  • x̄ is the sample mean
  • Z is the z-score for the desired confidence level
  • s is the sample standard deviation
  • n is the sample size

For example, let’s say we have a sample of 100 students and the sample mean is 70. The sample standard deviation is 10. We want to find a 95% confidence interval for the population mean. The z-score for a 95% confidence level is 1.96. Plugging these values into the formula, we get the following confidence interval:

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CI = 70 ± 1.96 * (10 / √100)
CI = 70 ± 1.96 * (10 / 10)
CI = 70 ± 1.96 * 1
CI = 70 ± 1.96
CI = (68.04, 71.96)

We are 95% confident that the population mean is between 68.04 and 71.96.

Finding a Confidence Interval for a Proportion

To find a confidence interval for a proportion, we need to know the following information:

  • The sample proportion
  • The sample size
  • The confidence level

Once we have this information, we can use the following formula to find the confidence interval:

CI = p̂ ± Z * √(p̂(1 - p̂) / n)

where:

  • CI is the confidence interval
  • p̂ is the sample proportion
  • Z is the z-score for the desired confidence level
  • n is the sample size

For example, let’s say we have a sample of 100 students and 60 of them are female. We want to find a 95% confidence interval for the population proportion of female students. The sample proportion is 0.6. The z-score for a 95% confidence level is 1.96. Plugging these values into the formula, we get the following confidence interval:


CI = 0.6 ± 1.96 * √(0.6(1 - 0.6) / 100)
CI = 0.6 ± 1.96

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