1. In an experiment two independent groups were asked to perform a task. In grou
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Question
1. In an experiment two independent groups were asked to perform a task. In group A there were 15 subjects and in Group B there were 13 subjects. There were 15 success in A and 2 successes in B. The appropriate Agresti-Coull 95% confidence interval for pa-pb is (using z(0.975) = 1.96.
A. (0.7888, 1.0536)
B. (0.7888, 1.0000)
C. (0.0000, 0.7888)
D. (0.0000, 1.0536)
E. (0.6500, 1.0423)
2. MULTIPLE CHOICE
The claim "the standard deviation of a population is greater than 12.6" is tested using
A. Chi Square statistic
B. z statistic
C. t statistic
D. q statistic
E. f statistic
3. TRUE OR FALSE:
When performing inference on population means we require that the data are normal or that the sample size is large (to use the Central Limit Theorem) so that the sample means have a sampling distribution that is at least approximately normal. The same conditions hold for performing intference on population variance(s).
Explanation / Answer
Using Minitab.
Test and CI for Two Proportions
Sample X N Sample p
1 15 15 1.000000
2 2 13 0.153846
Difference = p (1) - p (2)
Estimate for difference: 0.846154
95% CI for difference: (0.650024, 1)
Test for difference = 0 (vs 0): Z = 8.46 P-Value = 0.000
TRADITIONAL METHOD
given that,
sample one, x1 =15, n1 =15, p1= x1/n1=1
sample two, x2 =2, n2 =13, p2= x2/n2 = 0.153846
I.
standard error = sqrt( p1 * (1-p1)/n1 + p2 * (1-p2)/n2 )
where
p1, p2 = proportion of both sample observation
n1, n2 = sample size
standard error = sqrt( (1*0.1538/15) +(0.1538 * 0.8462/13))
=0.14235
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.1
from standard normal table, two tailed z /2 =1.64
margin of error = 1.64 * 0.14235
=0.233454
III.
CI = (p1-p2) ± margin of error
confidence interval = [ (1-0.1538) ± 0.233454 ]
= [ 0.6500, 1.0423]
E. (0.6500, 1.0423)
Q2.
A. Chi Square statistic
since the claim to test standard deviation of a population is greater than 12.6, we use Chi square to
compare variance data
Q3.
May not be true, this can't be applicable for variance
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