Question

1. Let X denote the age of an Engineering Statistics student at the University of Arkansas. It is believed that the mean age is 21 yr. Suppose we wish to perform a hypothesis test to determine if the mean is something other than 21 yrs using a sample of size 16 and a level of significance of 0.01. Suppose the sample mean is 23.93 yrs and the sample standard deviation is 4.0 yr. Is rejecting the null hypothesis in favor of the alternative the correct decision?

   	A.	No, because Z0 = 2.93 > Z0.005=2.58 (the test statistic Z0 is NOT in the critical region)
   	B.	Yes, because T0 = 2.93 < t0.005,15=2.95 (the test statistic T0 is in the critical region)
   	C.	No, because T0 = 2.93 < t0.005,15=2.95 (the test statistic T0 is NOT in the critical region)
   	D.	No, because Z0 = 2.93 > Z0.005=2.58 (the test statistic Z0 is in the critical region)

Answer 1

Given that, sample size ( n ) = 16

sample mean = 23.93 yrs

sample standard deviation = 4.0 yr

The null and the alternative hypotheses are,

Test statistic is,

t-critical value at significance level of 0.01 with degrees of freedom of 15 is, t^* = 2.95

Critical region : T₀ < -2.95 or T₀ > 2.95

In above case, the test statistic T₀ is Not in the critical region.

Since, test statistic = T₀ = 2.93 < 2.95

we fail to reject the null hypothesis.

Answer: C) No, because T0 = 2.93 < t0.005,15=2.95 (the test statistic T0 is NOT in the critical region)