Question: The producers of a new toothpaste claim that it prevents more cavities than other brands of toothpaste. A random sample of 60 people used the new toothpaste for 6 months. The mean number of cavities at their next checkup is $1.5$. In the general population, the mean number of cavities at a 6 -month checkup is \(1.73\,(\sigma =1.12)\).

1. Is this a one- or two-tailed test?
2. What are \(H_{0}\) and \(H_{2}\) for this study?
3. Compute \(z_{obt}\)
4. What is \(z_{cv}\) ?
5. Should \(H_{0}\) be rejected? What should the researcher conclude?
6. Determine the \(95 \%\) confidence interval for the population mean, based on the sample mean.

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