# 請問研究所統計問題

1. In multiple regression analysis, the general linear model

a. can not be used to accommodate curvilinear relationships between dependent variables and independent variables

b. can be used to accommodate curvilinear relationships between dependent variables and independent variables

c. must contain more than 2 independent variables

d. none of these alternatives is correct

2. For a uniform probability density function,

a. the height of the function can not be larger than one

b. the height of the function is the same for each value of x

c. the height of the function is different for various values of x

d. the height of the function decreases as x increases

3.A population has a mean of 300 and a standard of 18. A sample of 144 observations will be taken. The probability that the sample mean will be between 297 to 303 is?

4.It is known that the population variance equals 484. With a 0.95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is?

Rating

1. In multiple regression analysis, the general linear model

a. can not be used to accommodate curvilinear relationships between dependent variables and independent variables

b. can be used to accommodate curvilinear relationships between dependent variables and independent variables

c. must contain more than 2 independent variables

d. none of these alternatives is correct

[R] b.

"linear model" 的 "linear" 是對參數 (係數) 而言的.

事實上, 任一本標準教本都有提到這點!

2. For a uniform probability density function,

a. the height of the function can not be larger than one

b. the height of the function is the same for each value of x

c. the height of the function is different for various values of x

d. the height of the function decreases as x increases

[R] b.

不過, 說實在的, 這題目有小蟲!

"is the same for each value of x" 僅限於某個範圍內的 x,

絕不是整條數線的每一點.

3.A population has a mean of 300 and a standard of 18. A sample of 144 observations will be taken. The probability that the sample mean will be between 297 to 303 is?

[R] n=144, 不妨假設中央極限定理適用.

換言之,

P[297 < Xbar < 303]

= P[ (297-200)/(18/√144) < Z < (303-300)/(18/√144) ]

= P[ -2 < Z < 2 ]

≒ 0.9545

4.It is known that the population variance equals 484. With a 0.95 probability, the sample size that needs to be taken if the desired margin of error is 5 or less is?

[R] σ^2 = 484 ==> σ=22

題目沒寫清楚! 假設是要做群體平均數的推論, 又假設中央極限

定理可用, 也就是能做常態近似. 則

n >= (z* σ/E)^2 = (1.96*22/5)^2 = 74.37

故 n >= 75.