# A local politician, running for reelection, claims that the mean prison time for car thieves is less than the required 5 years

A local politician, running for reelection, claims that the mean prison time for car thieves is less than the required 5 years. A sample of 80 convicted car thieves was randomly selected, and the sample mean length of prison time was found to be 4.5 years, with a sample standard deviation of 1.25 years. At a = 0.10, test the politician’s claim. **Decide whether the normal distribution or the t-distribution should be used.**

**Solution: **

__STEP 1:__ The hypotheses are

_{}

__STEP 2__: This test corresponds to a left-tailed test. We’ll use a z-test because the sample size is big enough to use normal approximation

__STEP 4:__ The significance is_{}, and therefore, the critical value is_{}. The rejection region is_{}.

__STEP 5:__ The z-statistics is computed as

_{}

__STEP 6:__ We reject the null hypothesis. That means that we have enough evidence to support the claim, at the 0.1 significance level.

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