A random sample of 59 avocados is selected from an orchard and the weight of each avocado is measured. The mean weight is 288.3 grams and the standard deviation is 95.6 grams.Calculate the standard error.
Question
A random sample of 59 avocados is selected from an orchard and the weight of each avocado is measured. The mean weight is 288.3 grams and the standard deviation is 95.6 grams.Calculate the standard error.
Solution
The standard error (SE) is a measure of how much the sample mean is likely to vary from the true population mean. It can be calculated using the following formula:
SE = σ / sqrt(n)
where: σ is the standard deviation, and n is the sample size.
Given that the standard deviation (σ) is 95.6 grams and the sample size (n) is 59, we can substitute these values into the formula:
SE = 95.6 / sqrt(59)
Calculating the above expression gives us:
SE = 95.6 / 7.68 = 12.45 grams
Rounding to two decimal places, the standard error for this sample of avocados is 12.45 grams. This means that the sample mean is likely to vary from the true population mean by about 12.45 grams.
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