Question

A large university claims the mean number of classroom hours per week for full-time faculty is less than 9 hours per week. A random sample 11 faculty is selected from this university and found that the sample mean ¯x is 10 hours per week with a sample standard deviation of s = 2.15. Perform a hypothesis test for the claim at α = 0.05 level of significance?

(a) Hypothesis: H0 :

Ha :

(b) Test Statistics=

(c) Pvalue=

(d) The degrees of freedom, d.f=

(e) Decision:

(f) Conclusion:

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 9
Alternative Hypothesis, Ha: μ < 9

b)

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (10 - 9)/(2.15/sqrt(11))
t = 1.543

c)

P-value Approach
P-value = 0.9231

d)

df = 11 - 1 = 10

e)

As P-value >= 0.05, fail to reject null hypothesis.

f)

There is not sufficient evidence to conclude that mean number of classroom hours per week for full-time faculty is less than 9 hours per week.