The tensile strength of a fiber used in manufacturing cloth is of interest to th
ID: 3124393 • Letter: T
Question
The tensile strength of a fiber used in manufacturing cloth is of interest to the purchaser. Previous experience indicates that the standard deviation of tensile strength is 6 psi. A random sample of twelve fiber specimens is selected, and the average tensile strength is found to be 204 psi. Test the hypothesis that the mean tensile strength equals 200 psi versus the alternative that the mean exceeds 200 psi. Use alpha=0.05. What is the P-value for this test? Construct a 95% lower confidence interval on the mean tensile strength.Explanation / Answer
a)
Formulating the null and alternative hypotheses,
Ho: u <= 200
Ha: u > 200
As we can see, this is a right tailed test.
Thus, getting the critical t,
df = n - 1 = 11
tcrit = + 1.795884819
Getting the test statistic, as
X = sample mean = 204
uo = hypothesized mean = 200
n = sample size = 12
s = standard deviation = 6
Thus, t = (X - uo) * sqrt(n) / s = 2.309401077
As t > 1.7959, we REJECT THE NULL HYPOTHESIS.
Hence, there is significant evidence at 0.05 level that the average tensile strength is greater than 200 psi. [CONCLUSION]
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b)
Also, the p value is, using technology,
p = 0.020671134 [ANSWER]
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c)
For the 0.95 confidence level, then
df = 11
alpha = (1 - confidence level) = 0.05
t(alpha) = 1.795884819
lower bound = X - t(alpha) * s / sqrt(n) = 200.8894362
Hence, the confidence interval is
u > 200.889 psi [ANSWER]
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