Question 1204880: A sample of 19 scores are selected from a normally distributed population with a mean of μ= 98 and a standard deviation of σ= 15. Round your answers to one decimal place.
What is the cutoff value for the bottom 1% of possible sample means?
What is the cutoff value for the top 4% of possible sample means?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! sample mean is 98.
sample standard deviation is 15.
sample size is 19.
you would use the t-score for this because, even though the standard deviation is taken from the population, the sample size is less than 30.
those rules are debatable and not universally agreed upon.
follow the guidelines that you were taught.
standard error = standard deviation / sqrt(sample size) = 15/sqrt(19) = 3.4412.
if you use the t-score, you would do the following:
degrees of freedom = sample size minus 1 = 18
t-score with .01 area under the normal distribution curve to the left of it, with 18 degrees of freedom, is equal to -2.5524.
t-score formula of t = (x-m)/s becomes -2.5524 = (x-98)/3.4412.
solve for x to get x = -2.5524 * 3.4412 + 98 = 89.2167.
round to one decimal point to get 89.2.
t-score with .04 area under the normal distribution curve to the right of it, with 18 degrees of freedom, is equal to 1.8553.
t-score formula of t - (x-m)/s becomes 1.8553 = (x-98)/3.4412.
solve for x to get x = 1.8553 * 3.4412 + 98 = 104.3845.
round to one decimal point to get 104.4.
if you used the z-score formula, you would get the following.
z-score with 1% of the area under the normal distribution curve to the left of it is z = -2.3263
z-score formula of z = (x-m)/s becomes -2.3263 = (x-98)/3.4412.
solve for x to get x = -2.3263 * 3.4412 + 98 = 89.9947.
round to one decimal point to get 90.
z-score with 4% of the area under the normal distribution curve to the right of it is z = 1.7507
z-score formula of z = (x-m)/s becomes 1.7507 = (x-98)/3.4412.
solve for x to get x = 1.7507*3.4412 + 98 = 104.0245.
round to 1 decimal point to get 104.
if you used t-score, you would get 89.2 to 194.4.
if you used z-score, you would get 90 to 104.
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