The Following Display from a TI-84 Plus Calculator Presents the Results

question 6

Multiple Choice

The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population mean $\mu .$ State the null and alternate hypotheses.

• A) \(H _ { 0 } : \mu = 47 , H _ { 1 } : \mu < 47\)
• B) \(H _ { 0 } : \mu \neq 46.81 , H _ { 1 } : \mu = 46.81\)
• C) \(H _ { 0 } : \mu \neq 47 , H _ { 1 } : \mu = 47\)
• D) \(H _ { 0 } : \mu = 47 , H _ { 1 } : \mu = 46.81\)

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Definitions:

Population Proportions

The percentage or fraction of individuals in a population that exhibit a particular attribute or characteristic.

Null Hypothesis

A hypothesis in statistical testing that there is no effect or no difference, and any observed deviation is due to sampling or experimental error.

Significance Level

A threshold below which a p-value is considered statistically significant, indicating that observed results are unlikely to be due to chance.

Critical Value

The point or points on the scale of a test statistic beyond which we reject the null hypothesis; these values define the threshold of significance.