Question

1)S_M tries to estimate which of the following:

A) Population mean

B) Population standard deviation

C) distribution of sample mean's (DSM) standard error

D) Distribution of sample mean's (DSM) critical region

2)A t-value tries to estimate which of the following:

A) population mean

B) level of significance

C) df

D) z-score

3)Which of the following df values would make it so that the t -distribution looks most like the real Distribution of Sample Means (DSM)?

A) df = 8  

B) df = 20

C) df = 30

D) df=60

Answer 1

1.) Sm tries to estimate the

Ans. C. Distribution of the sample mean's (DSM) standard error.

2.) A t-value tries to estimate

Ans. D. Z-score. [ As T-distribution is also symmetrical for large n ]

3.) T-distribution looks most like the real Distribution of Sample Means (DSM) for

Ans. C and D. Df = 30 and Df = 60

(Reason: The most real distribution of sample means for a sample of sizes 30 or more is the normal symmetrical distribution by the Central Limit Theorem (CLT). The t-value has a degree of freedom = sample size - 1. A degree of freedom of 30 indicates that the sample size is 31 which is appropriate for the CLT to hold).

If only one option can be selected go for df=60 because larger the size of sample, more accurate is the symmetry.