Consider use of a Student\'s distribution to test the difference of means for in

Question

Consider use of a Student's distribution to test the difference of means for independent populations using random samples of sizes n_1 and n_2. (a) Which process gives the larger degrees of freedom, Satterthwalte's approximation or using the smaller of n_1 - 1 and n_2 - 1? Which method is more conservative? What do we mean by "conservative"? Note that computer programs and other technology commonly use satterthwalte's approximation. Satterthwalte's approximation is larger. This method is more conservative because it uses a larger degrees of freedom. Satterthwalte's approximation is smaller. Using the smaller of n_1 - 1 and n_2 - 1 is more conservative because it uses a larger degrees of freedom. Satterthwalte's approximation is larger. Using the smaller of n_1 - 1 and n_2 - 1 is more conservative because it uses a larger degrees of freedom. Satterthwalte's approximation is smaller. This method is more conservative because it uses a smaller degrees of freedom. (b) Using the same hypotheses and sample data. is the P-value smaller for larger degrees of freedom? How might a larger P-value impact the significance of a test? The P-value will be larger. Using a larger P-value might lead to concluding that a test is significant. The P-value will be smaller. Using a smaller P-value might lead to concluding that a test is significant. The P-value will be larger. Using a larger P-value might lead to concluding that a test is significant. The P-value will be smaller. Using a smaller P-value might lead to concluding that a test is significant.

Explanation / Answer

a)

Option (C) is correct.

Explanation -

The Satterwait's process has higher degree of freedom. It is more conservative to use smaller of n1-1 or n2-1. using smaller degrees of freedom means there is more area in the tails of the student t-distribution resulting in larger p-values.

--------------------------------------------------

b)

Option (D) is correct.

Explanation -

A large degree of freedom yields a small p-value.

A larger p-value might resultin a test that is not significant while a small p-value might result in significance as the probability of claim being true becomes more than the significance level at smaller degrees of freedom.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.