Consider the following printout. HYPOTHESIS: VARIANCE $X = x$
$$X = \text { gpa }$$
SAMPLE MEAN OF $\mathrm { X } = 2.8814$
SAMPLE VARIANCE OF $X = .21000$
SAMPLE SIZE OF $X = 250$
HYPOTHESIZED VALUE $( \mathrm { x } ) = 3.0$
VARIANCE $\mathrm { X } - \mathrm { x } = - .1186$
$$z = - 4.09209$$
Is this a large enough sample for this analysis to work?
A) Yes, since the population of GPA scores is approximately normally distributed.
B) Yes, since the $n p 15$ and $n q 15$.
C) Yes, since $n = 250$, which is greater than 30 .
D) No.

Question

Consider the following printout. HYPOTHESIS: VARIANCE $X = x$
$$X = \text { gpa }$$
SAMPLE MEAN OF $\mathrm { X } = 2.8814$
SAMPLE VARIANCE OF $X = .21000$
SAMPLE SIZE OF $X = 250$
HYPOTHESIZED VALUE $( \mathrm { x } ) = 3.0$
VARIANCE $\mathrm { X } - \mathrm { x } = - .1186$
$$z = - 4.09209$$
Is this a large enough sample for this analysis to work?
A) Yes, since the population of GPA scores is approximately normally distributed.
B) Yes, since the $n p > 15$ and $n q > 15$.
C) Yes, since $n = 250$, which is greater than 30 .
D) No.

Quizplus · Accepted Answer

The Central Limit Theorem states that if the sample size is large enough (usually $n > 30$), the distribution of the sample means will be approximately normally distributed regardless of the shape of the population distribution. Since the sample size here is 250, which is greater than 30, it is considered large enough for the analysis.

Consider the Following Printout X=xX = xX=x X= gpa X = \text { gpa }X= gpa

Consider the Following Printout $X = x$ $X = \text { gpa }$