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 used to estimate an unknown population mean based on a sample of data. The interval is constructed by taking a sample from a population, calculating the sample mean and standard deviation, and using this information to estimate the population mean. The t-interval is used when the population standard deviation is unknown.
Steps to construct a one-sample t-interval for population mean:
1. Define the level of confidence and find the t-value associated with it using the t-distribution table. For example, if the desired level of confidence is 95%, and the sample size is 20, the t-value would be 2.093.
2. Collect a sample of data from the population and calculate the sample mean and sample standard deviation.
3. Calculate the standard error of the mean using the formula: standard error = sample standard deviation / square root of sample size.
4. Calculate the margin of error using the formula: margin of error = t-value x standard error of the mean.
5. Calculate the lower and upper bounds of the interval using the formulas: lower bound = sample mean – margin of error and upper bound = sample mean + margin of error.
6. Interpret the estimated interval. For example, if the interval is (10, 20), we can interpret it as saying that with a 95% level of confidence, the true population mean falls between 10 and 20.
Some assumptions of the one-sample t-interval for population mean include:
1. The sample is randomly selected from the population.
2. The population follows a normal distribution.
3. The sample size is small (less than 30) or the population standard deviation is unknown.
4. The observations within the sample are independent of each other.
In conclusion, the one-sample t-interval for population mean is a useful tool for estimating an unknown population mean with a certain level of confidence. It is important to keep in mind the assumptions and steps involved in constructing the interval to ensure accurate results.
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