calculate the sampling distribution parameters U=120,O=unknown,s+8,n=25
To calculate the sampling distribution parameters, we need to understand the concepts of population mean, sample mean, standard deviation, and sample size.
1. Population Mean (μ): It represents the mean or average value of all the members in a population. In this case, the population mean is unknown.
2. Sample Mean (x̄): It represents the mean or average value of a sample taken from the population. The sample mean is calculated using the formula:
x̄ = ΣX / n
where ΣX is the sum of all individual values in the sample, and n is the sample size.
Given:
x̄ = 120 (sample mean)
s = 8 (sample standard deviation)
n = 25 (sample size)
3. Standard Deviation (σ): It measures the variability or spread of the data. In this case, the population standard deviation (σ) is unknown.
To calculate the sampling distribution parameters, we can use the Standard Error of the Mean (SEM) formula, which estimates the standard deviation of the sampling distribution.
Standard Error of the Mean (SEM) formula:
SEM = s / √n
where s is the sample standard deviation, and n is the sample size.
To find the value of SEM:
SEM = 8 / √25
= 8 / 5
= 1.6
Hence, the sampling distribution parameters are:
μ = 120 (sample mean)
σ = unknown (population standard deviation)
SEM = 1.6 (standard error of the mean)