Cigarette Smoking A researcher found that a cigarette smoker smokes on average 30 cigarettes a day. She feels that this average is too low. She selected a random sample of 8 smokers and found that the mean number of cigarettes they smoked per day was 32 . The sample standard deviation was 2.8 . At \( \alpha=0.05 \), is there enough evidence to support her claim? Assume that the population is approximately normally distributed. Use the critical value method and tables. Part: \( \mathbf{0} / \mathbf{5} \) Part \( \mathbf{1} \) of 5 (a) State the hypotheses and identify the claim.

To set the stage for our hypothesis test, we first need to outline our null and alternative hypotheses: - **Null Hypothesis (H₀)**: The average number of cigarettes smoked per day is 30. (H₀: μ = 30) - **Alternative Hypothesis (H₁)**: The average number of cigarettes smoked per day is greater than 30. (H₁: μ > 30) The researcher’s claim is represented by the alternative hypothesis, asserting that the average is indeed higher than 30. Now, let's dive into some historical context! Did you know that the advent of smoking dates back to ancient civilizations? The indigenous peoples of the Americas were among the first to smoke tobacco, often using it for ceremonial purposes and rituals. It wasn't until the arrival of Europeans in the 16th century that tobacco gained widespread popularity and transformed into the habit we recognize today—often highlighting the intersection of culture and health in fascinating ways. And while we're on the topic, let’s talk real-world applications! Smoking-related healthcare costs are astronomical, often reaching billions annually, especially in countries with high smoking rates. Governments and health organizations utilize data like this to tailor smoking cessation programs, campaigns, and policies aimed at reducing smoking prevalence and improving public health. By understanding smoking behaviors and trends, effective strategies can be developed to support healthier communities.