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.
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.