Estimating Population Mean using the One-Mean Z-Interval Procedure

when to use the one-mean z-interval procedure

The one-mean z-interval procedure is used when we want to estimate the population mean (μ) using a sample mean (x̄) and the standard deviation of the sample (σ) is known

The one-mean z-interval procedure is used when we want to estimate the population mean (μ) using a sample mean (x̄) and the standard deviation of the sample (σ) is known.

In order to use the one-mean z-interval procedure, we need to make sure that the following conditions are met:

1. Random Sample: The sample should be chosen randomly from the population of interest. This ensures that the sample is representative of the population.

2. Normality: The population should have a normal distribution, or the sample size should be large enough (usually n > 30) for the Central Limit Theorem to apply. If the sample size is small and the population is not normally distributed, alternative methods such as the t-distribution may be used instead.

Once we have met these conditions, we can calculate the confidence interval for the population mean using the following formula:

CI = x̄ ± z * (σ/√n)

Where:
CI represents the confidence interval
x̄ is the sample mean
z is the z-score related to the desired level of confidence (e.g., for a 95% confidence level, z = 1.96)
σ is the standard deviation of the population
n is the sample size

The resulting interval will provide an estimate of the true population mean with a specified level of confidence. For example, if we construct a 95% confidence interval, we can be 95% confident that the true population mean lies within the interval.

It is important to note that the one-mean z-interval procedure assumes that we have knowledge of the population standard deviation. If the population standard deviation is unknown, or if we are working with a small sample size (n < 30), we would need to use a different procedure, such as the one-mean t-interval procedure.

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