Question

The Acculturation Rating Scale for Mexican Americans (ARSMA) is a psychological test developed to measure the degree of Mexican/Spanish versus Anglo/English acculturation of Mexican Americans. The distribution of ARSMA scores in a population used to develop the test was approximately normal, with mean 3.0 and standard deviation 0.8. A further study gave ARSMA to 50 first-generation Mexican Americans. The mean of their scores is x bar = 2.36. If the standard deviation for the first-generation population is also 0.8, give a 95% confidence interval for the mean ARSMA score for first-generation

Answer 1

Mexican Americans. The mean of their scores is x bar = 2.36. If the standard deviation for the first-generation population is also 0.8, give a 95% confidence interval for the mean ARSMA score for first-generation Mexican Americans.

Answer 2

@jim_thompson5910

Answer 3

ok so we know xbar = 2.36, sigma = 0.8, mu = 3 (not used here but we might as well list it) and n = 50

Answer 4

ok

Answer 5

s = sigma/sqrt(n)

s = ???

Answer 6

s= .8/sqrt50

Answer 7

keep going

Answer 8

0.11314?

Answer 9

good

Answer 10

that's s

s = 0.11314

Answer 11

ok

Answer 12

now compute the upper and lower bounds

L = xbar - C*s
U = xbar + C*s

Answer 13

in this case, C = 1.96 (if you don't remember) because we're working with a 95% CI

Answer 14

so

xbar = 2.36
C = 1.96
s = 0.11314

Answer 15

whats c

Answer 16

C = 1.96

Answer 17

L =2.36 - 1.96
U = 2.36 plus 1.96

Answer 18

?

Answer 19

good, so

L = ??
U = ??

Answer 20

l=.4

Answer 21

4.32

Answer 22

LL: 2.36 minus 1.96 = 0.4
UL: 2.36 plus 1.96 = 4.32

Answer 23

oh wait...not sure why i didn't catch that typo

Answer 24

my bad

Answer 25

L = xbar - C*s
U = xbar + C*s

Answer 26

L = xbar - C*s
L = 2.36 - 1.96*0.11314
L = ???

Answer 27

So its LL= 2.1382456

Answer 28

good

Answer 29

U = xbar + C*s
U = 2.36 + 1.96*0.11314
U = ???

Answer 30

2.5817544

Answer 31

--> (2.1382456, 2.5817544) is the answer?

Answer 32

you got it

Answer 33

that's all there is to it with confidence intervals

Answer 34

thanks so much! i have two more proibs, ill repost