I have a large data set and I am asked to randomly generate 10 samples on a part
ID: 2932059 • Letter: I
Question
I have a large data set and I am asked to randomly generate 10 samples on a particular variable (GDP per capita). Each sample contains the observations for 10 countries.
I am then asked the question attached. I think the answer is that I should take (sample 1 mean (attached) - population mean)/sd. I am not sure if I take SD of population (8.97) or that divided by square root of n=10, or the standard error of the 10 sample means.
Population mean is 14.95, Sample 1 mean is 14.92. Population SD is 8.97, sample means SD is 1.47
Sample I Sample 2 Sample 3 Sample 4 Sample 5 Sample (6 Sample 7 Sample 8 Sample 9 Sample 10 Mean GDP/capita 14.92 18.18 15.15 15.59 17.83 16.79 13.44 16.68 14.95 15.04 Table 2: Descriptive Statistics of the Population GDP/cap Mean Standard Error Median Mode Standard Deviation Sample Variance Kurtosis Skewness Range Minimum Maximum Sum Count Confidence Level (95.0%) 14.94758065 1.138615056 14.35 24.4 8.965463916 80.37954323 0.804322993 0.314429655 35.45 0.95 36.4 926.75 62 2.27680152Explanation / Answer
The formula for calculating the test statistic is:
t = (x - µ) / SE
where x is sample mean, µ is population mean and SE is the standard error.
The formula for calculating the SE is:
SE = s * sqrt{ ( 1/n ) * [ ( N - n ) / ( N - 1 ) ] }
where s is the standard deviation of the sample, N is the population size, and n is the sample size.
The formula SE = s / sqrt( n ) is approximation which is applicable when population size is much larger(at least 20 times) than the sample size, which is not the case here as sample size is 10 and population size is 62.
So to calculate the SE in below formula:
SE = s * sqrt{ ( 1/n ) * [ ( N - n ) / ( N - 1 ) ] }
we need to know the standard deviation of the values in first sample of 10 observations.
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