Question

ALL PROBLEM SOLVING QUESTIONS NEED TP BE SHOWN/EXPLAINED. Please and thank you.

43.   For which of the following degrees of freedom is a t distribution closest to a normal distribution?

a. 10

b. 20

c. 5

d. 1000

44.   In order to construct a confidence interval for the difference between two means, we are going to assume which of the followings? (Select all that apply)

a. the two populations have the same variance.

b. the populations are normally distributed.

c. each value is sampled independently from each other value.

d. the two populations have similar means

45.   A researcher tries to compare grades earned on the first quiz by boys and girls. He randomly chooses 10 students from boys and 15 students from girls and calculates the confidence interval on difference between means. How many degrees of freedom will you get in this t distribution?

Answer 1

43. If the degrees of freedom in a t-distribution are greater than 30, we can assume it to be a normal distribution.

Correct option: D) 1000

44. To construct a confidence interval for the difference between two means, we will assume that the the populations have the same variance, the two populations are normally distributed and each value is sampled independently from each other value OR the samples are independent. Option D) is not a correct assumption.

Options A, B and C are correct

45. For a independent samples t-test,

df = n1 + n2 - 2
df = 10 + 15 - 2 = 25 - 2 = 23