Question

section 9.3 homework
score: 2/7 answered: 2/7
question 3
find the lower and upper $\chi^{2}$ critical values at 95% confidence and sample size 15. round to 3 decimal places.
lower:
upper:

Explanation:

Step1: Determine the degrees of freedom

The degrees of freedom \(df=n - 1\), where \(n = 15\). So \(df=15-1 = 14\).

Step2: Find the significance level

For a 95% confidence interval, the significance level \(\alpha=1 - 0.95=0.05\). The lower - tail area is \(\frac{\alpha}{2}=0.025\) and the upper - tail area is \(1-\frac{\alpha}{2}=0.975\).

Step3: Look up the critical values in the \(\chi^{2}\) - distribution table

Using the \(\chi^{2}\) - distribution table or a statistical software/ calculator:

• For the lower critical value with \(df = 14\) and area \(0.025\) in the left - tail, \(\chi_{0.025,14}^{2}=5.629\)
• For the upper critical value with \(df = 14\) and area \(0.975\) in the right - tail, \(\chi_{0.975,14}^{2}=26.119\)

Answer:

Lower: \(5.629\)
Upper: \(26.119\)