Hypothesis Testing Statistics Example 2

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

Example 2

hard
Continuing the light bulb example (H0:ฮผ=1000H_0: \mu = 1000, n=50n = 50, xห‰=985\bar{x} = 985, ฯƒ=40\sigma = 40), calculate the test statistic.

Solution

  1. 1
    Step 1: z=xห‰โˆ’ฮผ0ฯƒ/n=985โˆ’100040/50z = \frac{\bar{x} - \mu_0}{\sigma / \sqrt{n}} = \frac{985 - 1000}{40 / \sqrt{50}}.
  2. 2
    Step 2: 4050=407.07โ‰ˆ5.66\frac{40}{\sqrt{50}} = \frac{40}{7.07} \approx 5.66.
  3. 3
    Step 3: z=โˆ’155.66โ‰ˆโˆ’2.65z = \frac{-15}{5.66} \approx -2.65.

Answer

zโ‰ˆโˆ’2.65z \approx -2.65
The test statistic measures how many standard errors the sample mean is from the hypothesised value. A larger absolute z-value provides stronger evidence against 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 1 hard

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

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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