Question

here are summary statistics for randomly selected weights of newborn girls: ( n = 36 ), ( \bar{x} = 3197.2 ) g, ( s = 692.6 ) g. use a confidence level of 90% to complete parts (a) through (d) below.

a. identify the critical value ( t_{alpha/2} ) used for finding the margin of error.

( t_{alpha/2} = square )

(round to two decimal places as needed.)

Explanation:

Step1: Determine the degrees of freedom

The sample size \( n = 36 \), so the degrees of freedom \( df=n - 1=36 - 1 = 35 \).

Step2: Determine the significance level

The confidence level is \( 90\%=0.90 \), so the significance level \( \alpha=1 - 0.90 = 0.10 \). Then \( \alpha/2=0.05 \).

Step3: Find the critical value \( t_{\alpha/2} \)

We need to find the \( t \)-value with \( df = 35 \) and area in the right tail equal to \( 0.05 \). Using a \( t \)-distribution table or a calculator (such as the T.INV.2T function in Excel, where T.INV.2T(0.10,35)), we find that \( t_{0.05,35}\approx1.69 \).

Answer:

\( 1.69 \)