Hypothesis Testing Statistics Example 3

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

Example 3

hard
A school claims students sleep an average of 8 hours. A sample of 36 students has xห‰=7.5\bar{x} = 7.5 with ฯƒ=1.2\sigma = 1.2. State the hypotheses for a one-tailed test (testing if students sleep less) and compute the z-statistic.

Solution

  1. 1
    Step 1: H0:ฮผ=8H_0: \mu = 8, Ha:ฮผ<8H_a: \mu < 8.
  2. 2
    Step 2: z=7.5โˆ’81.2/36=โˆ’0.50.2=โˆ’2.5z = \frac{7.5 - 8}{1.2/\sqrt{36}} = \frac{-0.5}{0.2} = -2.5.

Answer

H0:ฮผ=8H_0: \mu = 8, Ha:ฮผ<8H_a: \mu < 8. z=โˆ’2.5z = -2.5.
A one-tailed test is used when we have a specific directional claim (students sleep less). The negative z-statistic supports the alternative hypothesis.

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 โ†’

More Hypothesis Testing Examples

Example 1 hard

A company claims its light bulbs last an average of 1000 hours. A sample of 50 bulbs has [formula] h

Example 2 hard

Continuing the light bulb example ([formula], [formula], [formula], [formula]), calculate the test s

Example 4 hard

In a two-tailed z-test at [formula], the test statistic is [formula]. Using critical values [formula

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