The following data represent the $\mathrm{pH}$ of rain for a random sample of 12 rain dates. A normal probability plot suggests the data could come from a population that is $\begin{array}{llll}5.30 & 5.72 & 4.38 & 4.80 \\ 5.02 & 4.57 & 4.74 & 5.19 \\ 4.61 & 4.76 & 4.56 & 5.68\end{array}$ normally distributed. A boxplot indicates there are no outliers. Complete parts a) through d) below. What happens to the interval as the level of confidence is changed? Explain why this is a logical result. As the level of confidence increases, the width of the interval This makes sense since the

Step 1 ：The question is asking about the effect of changing the level of confidence on the confidence interval. The confidence interval is a range of values, derived from a data set, which is likely to contain the value of an unknown population parameter. The width of the confidence interval gives us some idea about how uncertain we are about the unknown parameter. A wider interval may indicate that we need more data to get a precise estimate of the population parameter.

Step 2 ：The level of confidence reflects the degree of certainty we have that the parameter lies within the confidence interval. A higher level of confidence will result in a wider confidence interval. This is because to be more confident that we have captured the true population parameter, we need to allow for more potential values within the interval. Conversely, a lower level of confidence will result in a narrower confidence interval.

Step 3 ：To answer this question, we don't need to calculate anything, but rather explain the relationship between the level of confidence and the width of the confidence interval.

Step 4 ：Final Answer: As the level of confidence increases, the width of the confidence interval also increases. This is a logical result because to be more confident that the interval contains the true population parameter, we need to allow for more potential values within the interval. Conversely, if we want a narrower interval, we have to accept a lower level of confidence.