Question

You want to test H0: µ ≤ 10.00 against H1: π > 10.00 using α = 0.01, given that a sample of size = 25 found ?̅= 12.9 and s = 6.77.

a. What is the estimated standard error of ?̅, assuming that the null hypothesis is correct?

b. Should your test statistic be a Z or a T (which, ZSTAT or TSTAT)?

c. What is the attained value of the test statistic?

d. What is/are the critical values of the test statistic?

e. Is there sufficient evidence to say that µ is greater than 10?

Answer 1

a)

std.error = s/sqrt(n))
= 6.77/sqrt(25)
= 1.3540

b)

t stat as sample std deviation is given

c)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (12.9 - 10)/(6.77/sqrt(25))
t = 2.1418

d)
Rejection Region
This is right tailed test, for α = 0.01 and df = 24
Critical value of t is 2.492.
Hence reject H0 if t > 2.492

Rejection Region Approach
As the value of test statistic, t is within critical value range, fail to reject the null hypothesis

Conclusion
e)

There is not sufficient evidence to conclude that