Problem
Ages of Gamblers The mean age of a sample of 24 people who were playing the slot machines is 48.4 years, and the standard deviation is 6.8 years. The mean age of a sample of 33 people who were playing roulette is 55.4 with a standard deviation of 3.2 years. Can it be concluded at $\alpha=0.01$ that the mean age of those playing the slot machines is less than those playing roulette? Use $\mu_{1}$ for the mean age of those playing slot machines. Assume the variables are normally distributed and the variances are unequal. Part: $0 / 5$ Part 1 of 5 State the hypotheses and identify the claim with the correct hypothesis. \[ \begin{array}{l} H_{0}: \square(\text { Choose one) } \nabla \\ H_{1}: \square \text { (Choose one) } \nabla \end{array} \] This hypothesis test is a (Choose one) $\nabla$ test.
Solution
Step 1 ：State the hypotheses and identify the claim with the correct hypothesis. The hypotheses are as follows: \(H_{0}: \mu_{1} \geq \mu_{2}\) and \(H_{1}: \mu_{1} < \mu_{2}\).
Step 2 ：The claim is with the alternative hypothesis \(H_{1}\): \(\mu_{1} < \mu_{2}\).
Step 3 ：This hypothesis test is a left-tailed test.
