A computer package was used to generate the following printout for estimating the sale price of condominiumsin a particular neighborhood. $\begin{array}{rl}
\text { X}=&\text { sale-price }\
\
\text { SAMPLE MEAN OF X} =&46,600\
\text { SAMPLE STANDARD DEV }=&13,747\
\text { SAMPLE SIZE OF X }= &15\
\text { CONFIDENCE } = &99\
\
\text { UPPER LIMIT }= & 57,166.70 \
\text { SAMPLE MEAN OF X }= & 46,600 \
\text { LOWER LIMIT }= & 36,033.30
\end{array}$
What assumptions are necessary for any inferences derived from this printout to be valid?
A) The sample was randomly selected from an approximately normal population.
B) The sample variance equals the population variance.
C) The population mean has an approximate normal distribution.
D) All of these are necessary.

Question

A computer package was used to generate the following printout for estimating the sale price of condominiumsin a particular neighborhood. $\begin{array}{rl}
\text { X}=&\text { sale-price }\
\
\text { SAMPLE MEAN OF X} =&46,600\
\text {  SAMPLE STANDARD DEV }=&13,747\
\text {  SAMPLE SIZE OF X }= &15\
\text { CONFIDENCE } = &99\
\
\text { UPPER LIMIT }= & 57,166.70 \
\text { SAMPLE MEAN OF X }= & 46,600 \
\text { LOWER LIMIT }= & 36,033.30
\end{array}$ 
 What assumptions are necessary for any inferences derived from this printout to be valid?
A) The sample was randomly selected from an approximately normal population.
B) The sample variance equals the population variance.
C) The population mean has an approximate normal distribution.
D) All of these are necessary.

Quizplus · Accepted Answer

For inferences based on the sample mean and standard deviation to be valid, especially when constructing confidence intervals, it is necessary that the sample was randomly selected from a population that is approximately normal. This ensures that the sampling distribution of the mean is also approximately normal, which is a key assumption for many inferential statistics techniques. Assumptions about the sample variance being equal to the population variance or the population mean having an approximate normal distribution are not directly relevant in the context provided.

A Computer Package Was Used to Generate the Following Printout