A Random Sample of N Measurements Was Selected from a Population

question 88

Short Answer

A random sample of n measurements was selected from a population with unknown mean μ and known standard deviation σ. Calculate a 95% confidence interval for μ for the given situation. Round to the nearest hundredth when necessary. $n = 100 , \bar { x } = 58 , \sigma = 20$
A) $58 \pm 3.92$
B) $58 \pm 3.29$
C) $58 \pm 39.2$
D) $58 \pm 0.39$

• A) \(58 \pm 3.92\)
• B) \(58 \pm 3.29\)
• C) \(58 \pm 39.2\)
• D) \(58 \pm 0.39\)

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Definitions:

Statistical Significance

Refers to the likelihood that a result or relationship is caused by something other than mere random chance.

Sample Size

The number of participants or observations included in a study, which can affect the reliability and validity of the research findings.

True Population Value

The actual value of a parameter (e.g., mean, proportion) for the entire population being studied, which research attempts to estimate.

Probability

A measure of the likelihood that an event will occur, represented numerically between 0 (impossible) and 1 (certain).