Final answer:
Without knowing the degrees of freedom, which depend on the sample size, it is not possible to identify the correct chi-square score needed for a 95% confidence interval for the population standard deviation. The given chi-square scores are contingent upon this missing information.
Step-by-step explanation:
To determine which chi-square score should be used to construct a 95% confidence interval for the population standard deviation, one needs additional information that is not provided in the question: namely, the degrees of freedom (df), which typically are one less than the sample size (n - 1). However, given the question presents multiple-choice answers without this context, it implies that the necessary degrees of freedom might align with one of those values.
The 95% confidence interval is wider than the 90% confidence interval because it aims to cover a greater area under the curve, providing more certainty that it contains the true population parameter. Similarly, for chi-square distributions, a larger chi-square score corresponds to a wider confidence interval.
The choice among the given chi-square scores A. 29.05, B. 55.03, C. 44.55, and D. 62.42 would depend on the sample size and the associated degrees of freedom. Without this information, it is not possible to definitively select the correct chi-square score for the 95% confidence interval.