(i. Reasoning from a sample or small group to the entire group or population is called statistical inference.
(ii) A 95 percent confidence interval implies that about 95 out of 100 similarly constructed intervals will include the parameter being estimated.
(iii) For a sampling distribution of the means, 95% percent of the means would be between $\pm$ 1.96 standard deviations.
A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question

(i. Reasoning from a sample or small group to the entire group or population is called statistical inference. 
(ii) A 95 percent confidence interval implies that about 95 out of 100 similarly constructed intervals will include the parameter being estimated.
(iii) For a sampling distribution of the means, 95% percent of the means would be between $\pm$ 1.96 standard deviations.
A) (i), (ii), and (iii) are all correct statements.
B) (i) and (ii) are correct statements but not (iii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Quizplus · Accepted Answer

(i) Statistical inference indeed involves making conclusions about a population based on a sample. (ii) A 95% confidence interval means that if we were to take many samples and construct confidence intervals for each, about 95% of these intervals would contain the true population parameter. (iii) The statement about the sampling distribution of the means is a description of the central limit theorem, which states that the distribution of sample means will be normally distributed around the true population mean, with 95% of the means falling within 1.96 standard deviations of the true mean if the sample size is large enough.

(I Reasoning from a Sample or Small Group to the Entire