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The first step in this process is to calculate the standard error, which gives an estimate of the standard deviation of the sampling distribution. The formula for calculating the standard error (SE) is \(SE = \frac{s}{\sqrt{n}}\), where \(s\) is the standard deviation of the sample, and \(n\) is the sample size. Here, \(s = 3.75\) hours, and \(n = 40\). Therefore, \[SE = \frac{3.75}{\sqrt{40}} \]

The z-value for any given confidence level can be found from the standard normal distribution table or from a Z calculator. For a 98% confidence interval, the z-value is approximately 2.33, since it includes 98% of the data in a standard normal distribution, leaving 1% in each tail of the distribution.

The confidence interval is calculated as \(\mu = x \pm (Z * SE)\) where \(x\) is the sample mean, \(Z\) is the Z-value from the previous step, and \(SE\) is the standard error calculated in Step 1. Here, \(\mu = 23 \pm (2.33 * SE)\). The lower and upper bounds of the confidence interval are calculated by carrying out the plus and minus operations respectively.

The width of the confidence interval could be lessened in several ways: (1) Decrease the confidence level: A lower confidence level will result in a lower z-value, which would decrease the width of the confidence interval. However, this would also decrease the certainty about whether the true population parameter lies within the interval. (2) Increase the sample size: If the sample size is increased, it will decrease the standard error and hence, the width of the confidence interval will decrease. This is the preferred method because it keeps the confidence level the same while allowing for a narrower interval. (3) Lower the variability: If there is a way to control or eliminate the sources of variability in the sample data, this would lower the standard deviation (and hence the standard error) leading to a narrower confidence interval.

The best option would be to increase the sample size, as this would maintain the same level of confidence while lessening the width of the confidence interval. Lowering the variability could also be effective, but this might not be possible depending on the nature of the data. The method that sollicit decreasing the confidence level is less ideal since it forfeits some certainty in the process.