Question: The population time it takes a manufacturer to disassemble a product is normally distributed with the unknown population mean \(\mu \) and the unknown standard deviation \(\sigma \). A random sample of n = 81 products is observed and the sample mean time it took the manufacturer to disassemble them computed as \(\bar{X}=30\) minutes with the sample variance \({{s}^{2}}\) = 9 minutes.

1. Construct a 95% confidence interval, \(1-\alpha =0.95\) for the population mean
2. Construct a 98% confidence interval, \(1-\alpha =0.98\) for the population mean
3. Explain the effect of increasing confidence level on the confidence interval.

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