The heights of male college students are normally distributed with mean of 68 inches and standard deviation of 3 inches. If 80 samples consisting of 25 students each are drawn from the population, what would be the expected mean and standard deviation of the resulting sampling distribution of the mean
Answers
The mean of the sampling distribution of means is 68 in, whereas the standard error is 0.6 in.
Further explanation:
The population is normally distributed with mean 68 in and standard deviation 3 in. There were a total of 80 samples of size 25. Average height was collected for each sample and these averages comprise the sampling distribution of means.
Mean:
The mean of the sampling distribution (μ_{x}
x
) is equal to the mean of the population (μ).
μ_{x}
x
= μ = 68 in
Standard Deviation:
The standard error of the sampling distribution (σ_{x}
x
) is equal to:
σ_{x}
x
= [ σ ÷ \sqrt{n}
n
] * \sqrt{\frac{N-n}{N-1}}
N−1
N−n
where σ is the population standard deviation, N is the population size, and n is the sample size.
The term \sqrt{\frac{N-n}{N-1}}
N−1
N−n
is called "fpc" or "finite population correction". This is approximately equal to one if population size is large relative to the sample size. In that case, standard error is approximated by:
σ_{x}
x
= [ σ ÷ \sqrt{n}
n
] = 3 ÷ \sqrt{25}
25
= 3 ÷ 5 = 0.6 in
Learn more:
Learn more about mean: https://brainly.ph/question/1193782
Learn more about standard error: https://brainly.ph/question/2124347
Learn more about sampling distribution: https://brainly.ph/question/2147620
Keywords: mean, standard error, standard deviation, sampling distribution, statistics
Answer:
The mean of the sampling distribution of means is 68 in, whereas the standard error is 0.6 in.
Further explanation:
The population is normally distributed with mean 68 in and standard deviation 3 in. There were a total of 80 samples of size 25. Average height was collected for each sample and these averages comprise the sampling distribution of means.
Mean:
The mean of the sampling distribution (μ_{x}
x
) is equal to the mean of the population (μ).
μ_{x}
x
= μ = 68 in
Standard Deviation:
The standard error of the sampling distribution (σ_{x}
x
) is equal to:
σ_{x}
x
= [ σ ÷ \sqrt{n}
n
] * \sqrt{\frac{N-n}{N-1}}
N−1
N−n
where σ is the population standard deviation, N is the population size, and n is the sample size.
The term \sqrt{\frac{N-n}{N-1}}
N−1
N−n
is called "fpc" or "finite population correction". This is approximately equal to one if population size is large relative to the sample size. In that case, standard error is approximated by:
σ_{x}
x
= [ σ ÷ \sqrt{n}
n
] = 3 ÷ \sqrt{25}
25
= 3 ÷ 5 = 0.6