Question

question 3
1 pts
to estimate the proportion of library patrons who check out mystery novels, a librarian decides to gather a random sample of data and construct a 97% confidence interval. what critical value of the normal distribution should this librarian use when constructing this interval? choose the answer below that is most reasonable, given what you know about confidence intervals.
2.17
1.72
1.44
1.98
2.62

Explanation:

Step1: Calculate the significance level

The confidence level is \(C = 0.97\). The significance level \(\alpha=1 - C\). So, \(\alpha=1 - 0.97=0.03\).

Step2: Find the critical value \(z_{\alpha/2}\)

Since \(\alpha = 0.03\), then \(\alpha/2=\frac{0.03}{2}=0.015\). We need to find \(z\) such that \(P(Z>z_{\alpha/2})=\alpha/2 = 0.015\) and \(P(Z < z_{\alpha/2})=1 - 0.015=0.985\). Looking up in the standard normal table (or using a calculator with a normal - distribution function, e.g., \(z=\text{NORM.S.INV}(0.985)\) in Excel), we get \(z_{\alpha/2}\approx2.17\).

Answer:

2.17