Question 129929: Recently the national average yield on municipal bonds has been μ = 4.19%. A random sample of 16 Arizona municipal bonds gave an average yield of 5.11% with a sample standard deviation s = 1.15%. Does this indicate that the population mean yield for all Arizona municipal bonds is greater than the national average? Use α = 0.05. Assume x is normally distributed.
a) State the null and the alternate hypothesis.
b) Identify the sampling distribution to be used: the standard normal distribution or the Student's t distribution. Find the critical value(s).
c) Compute the z or t value of the sample test statistic.
d) Find the P value or an interval containing the P value for the sample test statistic.
e) Based on your answers to a through d, decide whether or not to reject the null hypothesis at the given significance level. Explain your conclusion in the context of the problem.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Recently the national average yield on municipal bonds has been μ = 4.19%. A random sample of 16 Arizona municipal bonds gave an average yield of 5.11% with a sample standard deviation s = 1.15%. Does this indicate that the population mean yield for all Arizona municipal bonds is greater than the national average? Use α = 0.05. Assume x is normally distributed.
a) State the null and the alternate hypothesis.
Ho: mu = 0.0419
Ha: mu > 0.0419
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b) Identify the sampling distribution to be used: the standard normal distribution or the Student's t distribution.
Ans: t-distribution because we are testing the population mean value.
Find the critical value(s).
One-tail test with alpha=5% and 15 df ; critical value: t =1.753
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c) Compute the z or t value of the sample test statistic.
t(5.11) = (0.0511- 0.0419)
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d) Find the P value or an interval containing the P value for the sample test statistic.
p-value = P(0.0419 <= t < 10 with 15 df) = 0.4836...
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e) Based on your answers to a through d, decide whether or not to reject the null hypothesis at the given significance level.
Since the p-value is greater than alpha, fail to reject Ho.
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Explain your conclusion in the context of the problem.
There is strong statistical evidence that we should not reject
the claim that mu = 4.19%
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Cheers,
Stan H.
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