Find the Smallest N Such That the Error Estimate in the Approximation

question 26

Multiple Choice

Find the smallest n such that the error estimate in the approximation of the definite integral $\int _ { 0 } ^ { 1 } 2 \sin \left( x ^ { 2 } \right) d x$ is less than $0.00001$ using the Trapezoidal Rule. Use a graphing utility to estimate the maximum of the absolute value of the second derivative.

• A) 208
• B) 189
• C) 196
• D) 201
• E) 188

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Definitions:

Type I Error

The incorrect rejection of a true null hypothesis, or a false positive, in statistical hypothesis testing.

P-value

A measure in hypothesis testing that indicates the probability of obtaining a result at least as extreme as the one observed, assuming the null hypothesis is true.

Null Hypothesis

A statement in inferential statistics that there is no effect or no difference, and any observed deviation from this state is due to chance.

Rejection Level

The threshold or critical value that determines whether to reject the null hypothesis in statistical hypothesis testing, often denoted by alpha.