Appendix A.33

Mean Hypothesis Test

Perform hypothesis tests for a single population mean using z or t distributions.

Hypothesis Test Calculator for Population Mean (t-test)

Perform t-tests when σ is unknown

Hypotheses

Null:
Alternative:
Degrees of Freedom:
df = 34

Calculations

Sample Mean
Standard Error
Critical Value
Test Statistic

t-Distribution Visualization (df = 34)

-1.6921.6920t₀ = -3.82Reject H₀Reject H₀Fail to Reject H₀

Classical Approach

Critical Region: t < -1.692 or t > 1.692
t₀ = -3.8168 is in rejection region

P-Value Approach

P-value = 0.0007
P-value < α = 0.05

Reject H₀

At the α = 0.05 significance level, there is sufficient evidence to conclude that the population mean differs from 98.6.