Hypothesis Testing Statistics Example 1

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

Example 1

hard
A company claims its light bulbs last an average of 1000 hours. A sample of 50 bulbs has xห‰=985\bar{x} = 985 hours with ฯƒ=40\sigma = 40. Set up the null and alternative hypotheses for a two-tailed test.

Solution

  1. 1
    Step 1: Null hypothesis H0H_0: ฮผ=1000\mu = 1000 (the claim is true).
  2. 2
    Step 2: Alternative hypothesis HaH_a: ฮผโ‰ 1000\mu \neq 1000 (the mean differs from the claim).
  3. 3
    Step 3: This is two-tailed because we are testing whether the mean is different (in either direction) from 1000.

Answer

H0:ฮผ=1000H_0: \mu = 1000, Ha:ฮผโ‰ 1000H_a: \mu \neq 1000 (two-tailed test).
Hypothesis testing starts by stating the null hypothesis (status quo or claim) and the alternative hypothesis (what we suspect). The test then determines if the data provides enough evidence to reject H0H_0.

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 2 hard

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

Example 3 hard

A school claims students sleep an average of 8 hours. A sample of 36 students has [formula] with [fo

Example 4 hard

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

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