Questions: Refer to the accompanying screen display that results from measured hemoglobin levels (g/dL) in 100 randomly selected adult males. The confidence level of 95% was used. Complete parts (a) through (c). 95% confidence interval results Variable Sample Mean Std. Error. DF L. Limit U. Limit Hemoglobin 13.465 1.436 99 13.180 13.750 a. What is the number of degrees of freedom that should be used for finding the critical value tα/2? There are 99 degrees of freedom. (Type a whole number.) b. Find the critical value tα/2 corresponding to a 95% confidence level. tα/2=1.96 (Round to two decimal places as needed.)

Refer to the accompanying screen display that results from measured hemoglobin levels (g/dL) in 100 randomly selected adult males. The confidence level of 95% was used. Complete parts (a) through (c). 95% confidence interval results Variable Sample Mean Std. Error. DF L. Limit U. Limit Hemoglobin 13.465 1.436 99 13.180 13.750 a. What is the number of degrees of freedom that should be used for finding the critical value tα/2? There are 99 degrees of freedom. (Type a whole number.) b. Find the critical value tα/2 corresponding to a 95% confidence level. tα/2=1.96 (Round to two decimal places as needed.)
Transcript text: Part 2 of 3 Points: 0 of 1 Save Refer to the accompanying screen display that results from measured hemoglobin levels ( $\mathrm{g} / \mathrm{dL}$ ) in 100 randomly selected adult males. The confidence level of $95 \%$ was used. Complete parts (a) through (c). $95 \%$ confidence interval results \begin{tabular}{|c|c|c|c|c|c|} \hline Variable & Sample Mean & Std. Error. & DF & L. Limit & U. Limit \\ \hline Hemoglobin & 13.465 & 1.436 & 99 & 13.180 & 13.750 \\ \hline \end{tabular} a. What is the number of degrees of freedom that should be used for finding the critical value $\mathrm{t}_{\alpha / 2}$ ? There are 99 degrees of freedom. (Type a whole number.) b. Find the critical value $t_{\alpha / 2}$ corresponding to a $95 \%$ confidence level. $t_{\alpha / 2}=1.96$ (Round to two decimal places as needed.)
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Solution

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Solution Steps

Step 1: Degrees of Freedom

The number of degrees of freedom used for finding the critical value \( t_{\alpha/2} \) is given as:

\[ \text{Degrees of freedom} = 99 \]

Step 2: Critical Value Calculation

To find the critical value \( t_{\alpha/2} \) corresponding to a \( 95\% \) confidence level, we use the formula:

\[ t_{\alpha/2} = t_{0.025, 99} \]

Using statistical tables or software, we find:

\[ t_{\alpha/2} \approx 1.98 \]

Final Answer

The answers to the questions are:

  • Degrees of freedom: \( \boxed{99} \)
  • Critical value \( t_{\alpha/2} \): \( \boxed{1.98} \)
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