In Exercise 9-20, find the boundary of the critical region if the type I error probability…
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Question “In Exercise 9-20, find the boundary of the critical region if the type I error probability…”
In Exercise 9-20, find the boundary of the critical region if the type I error probability is
9-20 A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed with standard deviation 0.25 volt, and the manufacturer wishes to test volts, using n = 8 units.
Answer
(a) Let denote critical values.
The distribution of the sample means is roughly normal with the , and the standard deviation
The z_values which correspond to the critical values are
We find that using the Cumulative Normal Distribution table, we can calculate and. Therefore,
![](https://drive.google.com/uc?id=1KmU2jZfYiEd5_LVN-PXgLJD2zmiIf_w-&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
The acceptance zone is therefore
![](https://drive.google.com/uc?id=1aOPYEAnmTHkHX8fuzXv3LCFOYTQNxnV_&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
.
![](https://drive.google.com/uc?id=1p10g6-RHUtw5AKIEvtnbckEVim8WFjh8&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=1LMFZAX3qN6tpn_sRqYtCYa8QQqM6InWs&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
. Therefore,
![](https://drive.google.com/uc?id=1WPo1DtxErVHDtgywdrzugE2B7qcMkQcC&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
We find
![](https://drive.google.com/uc?id=1qJGyu7VQDXbTcxC1bQTN-D8VDQ4GGLPj&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
and
![](https://drive.google.com/uc?id=1VJ1iRfBI3y15vZHNeLLDLyewUz5cagdr&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
in the Cumulative Normal Distribution table. Therefore,
![](https://drive.google.com/uc?id=1yc1FsKPkXgQtaJ3DWYuhXwq6bwj9GwKc&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
The acceptance zone is therefore
![](https://drive.google.com/uc?id=1kG1WjmzQNjSC7FDOPrvtGrXVdYSj8uq_&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
.
(c) n =16.
![](https://drive.google.com/uc?id=15_1H3bEgVVZiO97Os9EZvBE5K2PQf3H8&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
The zvalues which correspond to the critical values
![](https://drive.google.com/uc?id=1C8lVt9EAaBat_gQdpSipO8-SOcno2c3O&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
are
![](https://drive.google.com/uc?id=1o5LdfRxp_oYKdfdLKEe0FlT4tSDxIdg1&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=1PdCWjc_OrmImKdfAbFl4FScJU1P_q_uI&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=1JrhGcuv1ipol0sOuxeTgwYvcmZW52OM9&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
. Therefore,
![](https://drive.google.com/uc?id=1y8UccnmbF6qAY3b5Kf97ccQM9VJxi7Dc&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
We find
![](https://drive.google.com/uc?id=1cbLhPSRglr68FqIt4VMfYhyYQ7xksD-S&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
and
![](https://drive.google.com/uc?id=105MjLFGf8Lm1IdTbYlNrbCMIjfSa_tmm&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
in the Cumulative Normal Distribution table. Therefore,
![](https://drive.google.com/uc?id=18MKj42neNfq4E8qpw_BVzdMrEo7IDFwy&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
The acceptance zone is therefore
![](https://drive.google.com/uc?id=1-i8swCYF16mvRwJYRLXDdYO6GTXOJs3q&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
.
![](https://drive.google.com/uc?id=1rgiz7jrAL1mLMOOIXAx-7J4zhRsSzyga&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
![](https://drive.google.com/uc?id=1JKAy-vRZGQtMXOsYLS6vwUk5JCOqxd6J&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
. Therefore,
![](https://drive.google.com/uc?id=12kM5OmWnX3-pSSY--PmPRHP9vRctnVGJ&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
We find
![](https://drive.google.com/uc?id=1IXM8gdYdkAHvJJgxZ6QClCGRQFtIBu9P&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
and
![](https://drive.google.com/uc?id=1X1ihbOmZUKcVegDjyBNizC33whd2BHxJ&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
in the Cumulative Normal Distribution table. Therefore,
![](https://drive.google.com/uc?id=1_-Apiu466FxiooU7wtMtH-GgfhA3qflS&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
The acceptance zone is therefore
![](https://drive.google.com/uc?id=1zuDegoYlMpxyDbuNscYGUaTvJ59nrKP7&export=download/In-Exercise-9-20,-find-the-boundary-of-the-critical-region-if-the-type-I-error-probability.png?x-oss-process=image/resize,w_560/format,webp)
.
Conclusion
Above is the solution for “In Exercise 9-20, find the boundary of the critical region if the type I error probability…“. We hope that you find a good answer and gain the knowledge about this topic of math.