P-Value Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
A one-tailed test has z=1.7z=1.7. Find the p-value and determine if we reject H0H_0 at ฮฑ=0.05\alpha=0.05.

Solution

  1. 1
    One-tailed p-value: p=P(Z>1.7)=1โˆ’0.9554=0.0446p = P(Z > 1.7) = 1 - 0.9554 = 0.0446
  2. 2
    Compare to ฮฑ=0.05\alpha = 0.05: p=0.0446<0.05p = 0.0446 < 0.05
  3. 3
    Decision: Reject H0H_0 at ฮฑ=0.05\alpha = 0.05

Answer

p=0.0446<0.05p = 0.0446 < 0.05. Reject H0H_0 at 5% significance level.
For one-tailed tests, the p-value is the tail probability in the direction of Hโ‚. Since p < ฮฑ, the result is statistically significant โ€” data provides sufficient evidence to reject Hโ‚€ in favor of Hโ‚.

About P-Value

The probability of observing a test statistic at least as extreme as the one computed from the sample data, assuming the null hypothesis H0H_0 is true.

Learn more about P-Value โ†’

More P-Value Examples

Example 1 medium

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Example 2 hard

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Example 4 hard

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