A rowing team consists of four rowers who weigh 152, 156, 160, and 164 pounds. Find all possible random samples with replacement of size two and compute the sample mean for each one. Use them to find the sampling distribution of the sample mean. Also verify the results.
Answers
Explanation:
The mean of the sample mean ˉX that we have just computed is exactly the mean of the population. The standard deviation of the sample mean ˉX that we have just computed is the standard deviation of the population divided by the square root of the sample size: √10=√20/√2.
Answer:
We have population values 152, 156, 160, and 164 population size N=4 and sample size n=2. The number of possible samples which can be drawn without replacement is. ^{N}C_n=^{4}C_2=6. NCn=4C2=6.
Explanation:
The mean and standard deviation of the population {152,156,160,164}
in the example are μ=158
and σ=20−−√
. The mean of the sample mean X¯
that we have just computed is exactly the mean of the population. The standard deviation of the sample mean X¯
that we have just computed is the standard deviation of the population divided by the square root of the sample size: 10−−√=20−−√/2–√
. These relationships are not coincidences, but are illustrations of the following formulas
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