Null Hypothesis ($H_0$): The assumption that nothing changed. "Innocent until proven guilty." We build our baseline normal curve purely around this $H_0$ mean.
P-Value vs Alpha ($\alpha$): $\alpha$ is our fixed line in the sand (e.g., $5\%$). The P-Value is the area representing how rare our sample result is, *assuming* $H_0$ is true.
Decision Rule: If P-Value $\leq \alpha$, the evidence is too wildly rare to have happened by chance. We Reject $H_0$. If $P > \alpha$, we Fail to Reject $H_0$ (we don't "Accept" it, we just lack evidence to convict).
Tags
P-ValueNull HypothesisAlphaRejection Region
TEST STATISTIC
$Z = \frac{\bar{x} - \mu_0}{\sigma/\sqrt{n}}$
Null Hypothesis $H_0$ Dist
Alpha Rejection Zone
Sample $\bar{x}$ Result
Null Hypothesis Model
Assume $H_0: \mu_0$ = 50
Significance Line in the Sand
Your Random Sample Result
Observed Sample $\bar{x}$ = 52
ONE-SIDED Z-TEST ($H_a: \mu > \mu_0$)
Alpha Threshold:$\alpha = 0.05$
Sample Z-Score:Z = 1.33
P-Value Area:0.091 (9.1%)
CONCLUSION VERDICT
FAIL TO REJECT H₀
The Meaning: A P-value of 9.1% means that if $H_0$ was completely true, there's still a 9.1% chance we'd grab a random sample as extreme as this out of pure dumb luck. Since 9.1% > 5%, our evidence is "not rare enough" to formally convict. Let $H_0$ go!