Question

A sociologist is studying the number of years of education of students whose mothers have bachelor's degrees or higher. The data is normally distributed with a population mean of 14.5 years and a population standard deviation of 2.5 years. If a sample of 55 students is selected at random from the population, select the mean and standard deviation of the sampling distribution below.
Select all that apply

a. o-×=0.05 years
b. o-×= 2.5 years
c. o-×= 0.34 years
d. u-×= 14.5 years
e. u-×= 0.26 years
f. u-×= 1.96 years

Answer 1

TOPIC:Mean and standard deviation of the sample mean.

Here the population distroibution is years Normal, and with mean, m= 14.5 sd, o = 2.5 years, Here, na sample size = 55. Let, X., X2, –, X55 be the observations sample 55 . = sample mean. 55 -=E (8) = So, we have M = E(x) = E = 2 ) 2. 1. E(X) =My &i=160 55 55 m 55 k. sve 55. = var (7), Again, o

- t Due to 7 lindependence. vars (xi). - (8) intendente 552 I As, var (xi) = 82 ; & 1=1,2,- 155 5502 552 Hence, we get, V 35 5 years = 0.3371 years, - To 34 years, Answers - iM 21415 yeard go 0.34 Years & X