Hypothesis Testing Statistics Example 4

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

Example 4

hard
In a two-tailed z-test at α=0.05\alpha = 0.05, the test statistic is z=2.10z = 2.10. Using critical values ±1.96\pm 1.96, should H0H_0 be rejected?

Solution

  1. 1
    Step 1: In a two-tailed test at α=0.05\alpha = 0.05, we reject H0H_0 when ∣z∣>1.96|z| > 1.96.
  2. 2
    Step 2: Since ∣2.10∣>1.96|2.10| > 1.96, the test statistic falls in the rejection region, so we reject H0H_0.

Answer

Yes. Reject H0H_0 because z=2.10z = 2.10 is beyond the critical value.
Hypothesis test decisions can be made by comparing the test statistic to a critical value or by comparing a p-value to alpha. Both approaches answer the same decision question.

About Hypothesis Testing

Hypothesis testing is a formal statistical procedure for using sample data to decide between two competing claims about a population parameter. You state a null hypothesis (no effect) and an alternative hypothesis, collect data, compute a test statistic, and determine whether the evidence is strong enough to reject the null.

Learn more about Hypothesis Testing →

More Hypothesis Testing Examples

Example 1 hard

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Example 2 hard

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Example 3 hard

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