_____ 40. How does the t-model compare to the Normal model for various sample si

Question

_____ 40. How does the t-model compare to the Normal model for various sample sizes?
a. As the sample size decreases, the t-model comes closer to approximating a Normal model.
b. The larger sample sizes increase the variation so the t-model and Normal model become more similar.
c. As the sample size increases, the t-model comes closer to approximating a Normal model.
d. The difference between the two is the degrees of freedom.

_____ 41. It is expected that a quarter of the responses to the question “Do you enjoy being a parent?” will be “unsure” and there will be twice as many “yes” as “no” responses. Find the expected distribution for 86 responses.
a. Yes: 0.5; No: 0.25; Not Sure: 0.25
b. Yes: 42; No: 22; Not Sure: 22
c. Yes: 50%; No: 25%; Not Sure: 25%
d. Yes: 43; No: 21.5; Not Sure: 21.5

Explanation / Answer

Solution(40): According to center limit theorem, when the sample size is sufficiently large any distribution behaves like a normal distribution. The same goes with the t-model also. As the sample size increases, the t-model comes closer to approximating a normal model. Hence the correct option is Option (c).

Solution(41): As given, the quarter of total response is unsure. So the number of "unsure" responses = 86*0.25 = 21.5

Further it given that there will be twice as many "yes" as "no" responses. So the number of "no" responses = (86-21.5)/3 = 21.5

And the number of "yes" responses = 86 - (21.5+21.5) = 43.

Hence the expected distribution for 86 responses: "yes"=43, "no"= 21.5 and "unsure"= 21.5. Therefore the correct option is Option (d).

Related Questions

Navigate

• Browse (All)
• Browse #
• Subjects

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