Solution Found!
A random sample of 175 measurements possessed a mean = 8.2
Chapter 7, Problem 114SE(choose chapter or problem)
A random sample of 175 measurements possessed a mean \(\bar{x}=8.2\) and a standard deviation s = .79.
a. Test \(H_{0}: \mu=8.3\) against \(H_{\mathrm{a}}: \mu \neq 8.3\). Use \(\alpha=.05\).
b. Test \(H_{0}: \mu=8.4\) against \(H_{\mathrm{a}}: \mu \neq 8.4\). Use \(\alpha=.05\).
c. Test \(H_{0}: \sigma=1\) against \(H_{\mathrm{a}}: \sigma \neq 1\). Use \(\alpha=.05\).
d. Find the power of the test, part a, if \(\mu_{\mathrm{a}}=8.5\).
Text Transcription:
bar{x} = 8.2
H_0: mu = 8.3
H_a: mu neq 8.3
alpha = .05
H_0: mu = 8.4
H_a: mu neq 8.4
H_0: sigma = 1
H_a: sigma neq 1
mu_a = 8.5
Questions & Answers
QUESTION:
A random sample of 175 measurements possessed a mean \(\bar{x}=8.2\) and a standard deviation s = .79.
a. Test \(H_{0}: \mu=8.3\) against \(H_{\mathrm{a}}: \mu \neq 8.3\). Use \(\alpha=.05\).
b. Test \(H_{0}: \mu=8.4\) against \(H_{\mathrm{a}}: \mu \neq 8.4\). Use \(\alpha=.05\).
c. Test \(H_{0}: \sigma=1\) against \(H_{\mathrm{a}}: \sigma \neq 1\). Use \(\alpha=.05\).
d. Find the power of the test, part a, if \(\mu_{\mathrm{a}}=8.5\).
Text Transcription:
bar{x} = 8.2
H_0: mu = 8.3
H_a: mu neq 8.3
alpha = .05
H_0: mu = 8.4
H_a: mu neq 8.4
H_0: sigma = 1
H_a: sigma neq 1
mu_a = 8.5
ANSWER:Answer
Step 1 of 4
(a)
A random sample of measurements possessed a mean
Test
In hypothesis testing, the general form for a two-tailed test about a population mean is
as follows:
Rejection rule for a two-tail test: The Critical Value Approach,
……..(1)
Hence the test statistic for hypothesis tests about a population mean when is known,
We know
………..(2)
The rejection region requires in the two tail of the
From the table II, Appendix D, the value of
………..(3)
From equation (2) and (3) we can see that the observed value of the test statistic does not fall in the rejection region.
Since the rejection rule is not satisfying here,
[not possible condition]
Hence is not rejected and there is insufficient evidence to indicate the mean is different from
at