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Target: To check if the assumed μ0 is statistically correct, based on a sample average.
You don't know the standard deviation, hence you use the sample standard deviation.
|The population expected mean is known|
|Sample standard deviation|
The following R code should produce the same results:
Currently, there is no direct R function for the one-sample z test.
1. Two-tailed test
A farmer calculated last year the average of the apples' weight in his apple orchard μ0 equals 17 kg, based on the entire population.
The current year he checked a small sample of apples and the sample average x̅ equals 18 kg
Has the average of the apple's weight changed this year?
The farmer calculates the sample standard deviation of the apple's weight.
2. Left-tailed test.
In the same example as above, the farmer only cares to know if the entire average is lesser this year.