Question

UNAM is known to have a completion rate of 35% with a variance of 6.25%. A Research from
NRCT claims that the variance of UNAM completion rate is not as reported. A sample of 26
students found to have a completion rate of 37% with a variance of 7.29%. (Show all your work
and hypothesis clear steps)

a) Test the Researcher's claims at the 90% level of confidence [14]
b) Construct a 95% confidence interval for the population standard deviation. [6]

Answer 1

(a)

H0: Null Hypothesis: ² = 0.0625

HA: Alternative Hypothesis:

n = 26

s² = 0.0729

Test Statistic is given by:

= 0.10

ndf = n - 1 = 26 - 1 = 25

From Table, the Rejection Region for the Two Tail Test is:

R = {: < 14.611 OR > 37.652}

Since calculated value of is not in the critical region, the difference is not significant. Fail to reject null hypothesis.

The data do not support the claim that the variance of UNAM completion rate is not as reported.

(b)

n = 26

s² = 0.0729

= 0.05

ndf = 25

Confidence interval:

Low End

From Table:

Low End:

High End:
From Table,

High End:

So,

Confidence Interval:

0.2117 < < 0.3727