Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
9th Edition
ISBN: 9798214004020
Author: Jay L. Devore
Publisher: Cengage Learning US
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Textbook Question
Chapter 9.2, Problem 34E
Consider the pooled t variable
which has a t distribution with m + n − 2 df when both population distributions are normal with σ1 = σ2 (see the Pooled t Procedures subsection for a description of Sp).
a. Use this t variable to obtain a pooled t confidence interval formula for μ1 − μ2.
b. A sample of ultrasonic humidifiers of one particular brand was selected for which the observations on maximum output of moisture (oz) in a controlled chamber were 14.0, 14.3, 12.2, and 15.1. A sample of the second brand gave output values 12.1, 13.6, 11.9, and 11.2 (“Multiple Comparisons of Means Using Simultaneous Confidence Intervals,” J. of Quality Technology, 1989: 232–241). Use the pooled t formula from part (a) to estimate the difference between true average outputs for the two brands with a 95% confidence interval.
c. Estimate the difference between the two μ’s using the two-sample t interval discussed in this section, and compare it to the interval of part (b).
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Students have asked these similar questions
Assume the samples are random and independent, the populations are normally distributed, and the population variances are equal. The table available below shows the prices (in dollars) for a sample of automobile batteries. The prices are classified according to battery type. At α=0.10, is there enough evidence to conclude that at least one mean battery price is different from the others? Complete parts (a) through (e) below.
A statistician has a random sample of 30 observations from a
population which has a normal distribution with a standard deviation
of 5. These data are used to test the hypotheses
H : μ = 0, H, :μ + 0,
where is the mean of the population. A 5% significance level will be
used.
fl
(a) Calculate the power of an appropriate test when the true value of
the population mean is 2. Give your answer to 3 dp.
(b)
When the true value of the population mean is 3, the power of the
test at the 5% level is 0.908 (to 3 dp). Give an explanation of
what this means in terms of hypothesis testing.
(c) If the significance level of the test described in part (b) is
increased from 5% to 10% what effect will this have on the power?
Explain your answer.
Let (x1,x2,...,xn) be i.i.d. samples from a distribution with
mean μ and variance o². Consider the following estimator of µ:
леж
i=1
Σ₁=₁ ixi
Σ11
(a) Show that µ* is an unbiased estimator of μ.
(b) Explain why the above estimator u* is less preferable compared to
using the sample average à as an estimator for μ.
Hint: Show that * has a larger mean squared error.
Note that x
n(n+1)(2n +1)/6.
(1/n) (Σï=1 xi), Σ₁_₁ i n(n+1)/2 and Σ₁²
i=1
Chapter 9 Solutions
Student Solutions Manual for Devore's Probability and Statistics for Engineering and the Sciences, 9th
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