# Question: For large numbers of degrees of freedom we can approximate

For large numbers of degrees of freedom, we can approximate critical values of x2 as follows:

Here k is the number of degrees of freedom and z is the critical value(s) found from technology or table A-2. In Exercise 5 we have df = 35, so table A-4 does not list an exact critical value. If we want to approximate a critical value of x2 in the left-tailed hypothesis test with α = 0.05 and a sample size of 36, we let k = 35 with z = -1.645. Use this approximation to estimate the critical value of x2for Exercise 5. How close is it to the value of x2 = 22.465 obtained by using STATDISK and Minitab?

Here k is the number of degrees of freedom and z is the critical value(s) found from technology or table A-2. In Exercise 5 we have df = 35, so table A-4 does not list an exact critical value. If we want to approximate a critical value of x2 in the left-tailed hypothesis test with α = 0.05 and a sample size of 36, we let k = 35 with z = -1.645. Use this approximation to estimate the critical value of x2for Exercise 5. How close is it to the value of x2 = 22.465 obtained by using STATDISK and Minitab?

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