Question

6. A random sample of size 16 drawn from a normal population yielded the following results: 7--0.06, S = 1.07. a. Test Hop-O vs. 8:<@ 2-0.001. b. Estimate the observed significance of the test in part (a) and state a decision based on the p-value approach to hypothesis testing.

Answer 1

a)

Below are the null and alternative Hypothesis,
Null Hypothesis: μ = 0
Alternative Hypothesis: μ < 0

Rejection Region
This is left tailed test, for α = 0.001 and df = 15
Critical value of t is -3.733.
Hence reject H0 if t < -3.733

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (-0.96 - 0)/(1.07/sqrt(16))
t = -3.589

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

b)

P-value Approach
P-value = 0.0013
As P-value >= 0.001, fail to reject null hypothesis.