Calculating A One Sample T-Interval For Population Mean: A Statistical Technique For Estimating Mean Value With Confidence

One Sample T-Interval for Population Mean INTERVAL

1. Random sample or assignment2. 10% Condition n ≤ 1/10(N)3. Large counts: Po(n) ≥ 10 and (1-Po)(n) ≥ 10

A one sample t-interval for population mean is a statistical technique used to estimate the mean value of a population based on a sample mean. This interval provides a range of values that is likely to contain the true population mean, with a certain degree of confidence or probability.

The steps to calculate a one sample t-interval for population mean are:

1. Determine the sample size, mean, and standard deviation: Collect a sample of data from the population of interest and calculate the sample size (n), sample mean (x̄), and sample standard deviation (s).

2. Determine the level of confidence: Select a level of confidence, typically 95%, which represents the proportion of intervals that will contain the true population mean if we repeat the process multiple times.

3. Determine the degrees of freedom: Calculate the degrees of freedom (df), which is equal to n – 1.

4. Determine the critical value: Using the table of t-distribution values or a software package, determine the critical value for the given level of confidence and degrees of freedom.

5. Calculate the standard error: Divide the sample standard deviation by the square root of the sample size to obtain the standard error (SE).

6. Calculate the margin of error: Multiply the critical value by the standard error to obtain the margin of error (ME).

7. Calculate the confidence interval: Add and subtract the margin of error from the sample mean to obtain the confidence interval for the population mean.

The formula for the one sample t-interval for population mean is:

CI = x̄ ± t* (s / sqrt(n))

where CI is the confidence interval, x̄ is the sample mean, s is the sample standard deviation, n is the sample size, and t* is the critical value from the t-distribution.

In conclusion, a one sample t-interval for population mean is a valuable statistical tool that provides a range of values that is likely to contain the true population mean, given a certain level of confidence and sample data.

More Answers: