Researchers surveyed a simple random sample of $120$ college students in Brazil. $60$ students were given a single $100$-real note, while the other $60$ received the same amount in smaller denominations (five $20$-real notes). Among the single-note group, $48$ students spent some or all of the money. In the small-denomination group, $55$ students spent some or all of the money. Using a hypothesis test at the $0.05$ significance level, test the claim that fewer students spend the money when given a single large note.

Researchers are studying blood lead levels in two groups: children living near a highway with $n=35$, $\bar{x}=8.2\mu \text{g/dL}$, and $s=3.9\mu \text{g/dL}$, and children living in rural areas with $n=35$, $\bar{x}=1.1\mu \text{g/dL}$, and $s=3.3\mu \text{g/dL}$. Suppose an $F$ test was used at the $0.05$ significance level to test the claim that the variation in blood lead levels is greater for children living near the highway than for those in rural areas. Also, the rural group data consists of the following values (in $\mu \text{g/dL}$) : $2$, $2$, $12$, $15$, $6$, and $30$ other values that are all $0$.

Does this sample appear to be from a normally distributed population? If not, how does this affect the conclusion from the $F$ test?

A study investigates the effectiveness of a new safety helmet for cyclists. Out of $1800$ cyclists not wearing the new helmet, $27$ suffered serious head injuries. Out of $5400$ cyclists wearing the new helmet, $9$ suffered serious head injuries. At the $0.05$ significance level, test the claim by constructing an appropriate confidence interval that the new helmet reduces the risk of serious head injury.