Exhibit 10.6.A university wants to compare out-of-state applicants' mean SAT math scores (μ₁)to instate applicants' mean SAT math scores (μ₂).The university looks at 35 instate applicants and 35 out-of-state applicants.The mean SAT math score for instate applicants was 540,with a standard deviation of 20.The mean SAT math score for out-of-state applicants was 555,with a standard deviation of 25.It is reasonable to assume the corresponding population standard deviations are equal. Refer to Exhibit 10.6.To calculate the confidence interval for the difference μ₁ - μ₂,what is the number of degrees of freedom of the appropriate probability distribution? A)64 B)64.87 C)68 D)69

Question

Quizplus · Accepted Answer

The appropriate probability distribution is the t-distribution, and the number of degrees of freedom can be calculated as:
df = (s1^2/n1 + s2^2/n2)^2 / [ (s1^2/n1)^2 / (n1-1) + (s2^2/n2)^2 / (n2-1) ]
Plugging in the values, we get:
df = (20^2/35 + 25^2/35)^2 / [ (20^2/35)^2 / (35-1) + (25^2/35)^2 / (35-1) ]
df ≈ 68. Therefore, the answer is C.