Giant weta, native to New Zealand, are among the largest insects in the world. Their weight is normally distributed with mean of 25 g and standard deviation of 1.9 grams.A random sample of 10 giant weta is obtained. What is the standard error of the sample mean?(Give the answer to 3 decimal places.)
Question
Giant weta, native to New Zealand, are among the largest insects in the world. Their weight is normally distributed with mean of 25 g and standard deviation of 1.9 grams.A random sample of 10 giant weta is obtained. What is the standard error of the sample mean?(Give the answer to 3 decimal places.)
Solution
The standard error of the sample mean is calculated using the formula:
SE = σ / √n
where: SE = standard error σ = standard deviation n = sample size
In this case, the standard deviation (σ) is 1.9 grams and the sample size (n) is 10.
Substituting these values into the formula gives:
SE = 1.9 / √10
Calculating the square root of 10 gives approximately 3.162.
So, SE = 1.9 / 3.162
This gives a standard error of approximately 0.600 grams.
Rounded to three decimal places, the standard error of the sample mean is 0.600.
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