Practice Hypothesis Testing in Statistics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

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.

Hypothesis testing is like a courtroom trial for data. You start by assuming innocence (null hypothesis: nothing special is happening). Then you look at the evidence (data). If the evidence is strong enough to be very unlikely under the assumption of innocence, you reject it and conclude something real is happening.

Example 1

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

Example 2

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

Example 3

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

Example 4

hard
In a two-tailed z-test at \alpha = 0.05, the test statistic is z = 2.10. Using critical values \pm 1.96, should H_0 be rejected?
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