Answer the Question $\mathrm { n }$ Is Large $\mathrm { n }$

question 48

Multiple Choice

Answer the question.
-Many calculators or computers cannot directly calculate 70 ! or higher. When $\mathrm { n }$ is large, $\mathrm { n }$ ! can be approximated by $\mathrm { n } ! = 10 ^ { \mathrm { K } }$ , where $\mathrm { K } = ( \mathrm { n } + 0.5 ) \log \mathrm { n } + 0.39908993 - 0.43429448 \mathrm { n }$ . Evaluate 78 ! using the approximation given above.

• A) \(1.151 \times 10 ^ { 2 }\)
• B) \(1.131 \times 10 ^ { 115 }\)
• C) \(1.281 \times 10 ^ { 114 }\)
• D) \(3.356 \times 10 ^ { 308 }\)

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Definitions:

One-tail

Refers to a type of statistical test where the critical area of a distribution is one-sided so that it tests for the possibility of the relationship in one direction.

Two-tail

Refers to a type of statistical test that considers both the lower and upper tails of the distribution to determine significance.

Kruskal-Wallis Test

A non-parametric method for testing whether samples originate from the same distribution, used when the ANOVA assumptions are not met.

Wilcoxon Rank Sum Test

A non-parametric test used to compare two independent groups and determine if there are differences in their population median values.