The U.S. Department of Education is concerned with rising costs of a college edu
ID: 3180609 • Letter: T
Question
The U.S. Department of Education is concerned with rising costs of a college education. They take a random sample of 67 two-year public colleges in the U.S. and found the average tuition charged per semester in 2014-2015 was $2816 with standard error $109.097. A histogram of these costs yielded a right-skewed shape.
(a) Are the conditions met for constructing a confidence interval? (Check all that apply.)
The colleges were randomly chosen.
None of the conditions are met.
The Nearly Normal condition is met because the sample size is large enough for the data to be considered nearly normal.
The Nearly Normal condition is met because the sample size is large enough for the population to be considered nearly normal.
It is reasonable to assume that costs at different colleges were independent of each other.
The Nearly Normal condition is met because x-bar is nearly normal.
Explanation / Answer
we are able to use the normal distribution to construct our confidence interval because of the Central Limit Theorem. When n30, the sampling distribution of the sample mean becomes normal. If n30, the skewness of the population could influence the shape of the sampling distribution and make it not normal.
if the data is right skewed the normal conditions are not met.
None of the conditions are met.
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