An experimenter is interested in the hypothesis testing problem H_0: mu = 430.0
ID: 3153885 • Letter: A
Question
An experimenter is interested in the hypothesis testing problem H_0: mu = 430.0 versus H_A: mu notequalto 430.0 where mu is the average breaking strength of a bundle of wool fibers. Suppose that a sample of n = 20 wool fiber bundles is obtained and their breaking strengths are measured. For what values of the t-statistic does the experimenter accept the null hypothesis with a size alpha = 0.10? For what values of the t-statistic does the experimenter reject the null hypothesis with a size alpha = 0.01? Suppose that the sample mean is x = 436.5 and the sample standard deviation is s = 11.90. Is the null hypothesis accepted or rejected with alpha = 0.10? With alpha = 0.01? Write down an expression for the p-value and evaluate it using a computer package.Explanation / Answer
a)
As df = n - 1 = 19, then for two tailed, 0.10 level, using table/technology, the non-rejection region is
-1.729132812 < t < 1.729132812 [ANSWER]
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B)
As df = n - 1 = 19, then for two tailed, 0.01 level, using table/technology, the rejection region is
t < -2.860934606 OR t > 2.860934606 [ANSWER]
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c)
Formulating the null and alternative hypotheses,
Ho: u = 430
Ha: u =/ 430
As we can see, this is a two tailed test.
df = n - 1 = 19
Getting the test statistic, as
X = sample mean = 436.5
uo = hypothesized mean = 430
n = sample size = 20
s = standard deviation = 11.9
Thus, t = (X - uo) * sqrt(n) / s = 2.442763337
Using part a), we REJECT Ho at 0.10 level. [ANSWER]
Using part b), we ACCEPT HO at 0.01 level. [ANSWER]
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d)
Also, the p value is, using table,
0.02 < P < 0.05 [ANSWER]
Using technology,
p = 0.024517374 [ANSWER]
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