Question

The liquid chlorine added to swimming pools to combat algae has a relatively short shelf life before it loses its effectiveness. Records indicate that the mean shelf life of a 4.5-liter (L) jug of chlorine is 2160 hours (90 days). As an experiment, Holdlonger was added to the chlorine to find whether it would increase the shelf life. A sample of nine jugs of chlorine had these shelf lives (in hours):

2161

2173

2173

2180

2185

2170

2179

2164

2198

At the 0.025 level, has Holdlonger increased the shelf life of the chlorine?

a. What is the decision rule? (Round the final answer to 3 decimal places.)

Reject H₀: μ ≤ 2160 and accept H₁: μ > 2160 when the test statistic is  (Click to select)  greater than, less than, equal to

b. Compute the value of the test statistic. (Round the final answer to 2 decimal places.)

Value of the test statistic   

c. What is your decision regarding H₀?

(Click to select)  Reject  Fail to reject  H₀.

d. Determine or estimate the p-value.

The p-value is  (Click to select)  close to zero, zero, one.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 2160
Alternative Hypothesis, Ha: μ > 2160

a)
This is right tailed test, for α = 0.025 and df = 8
Critical value of t is 2.306.
Hence reject H0 if t > 2.306

b)
Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (2175.89 - 2160)/(11.2522/sqrt(9))
t = 4.237

c)
Reject H0

d)
P-value = 0.0014