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StatisticsQ&A LibraryThe article “Supply Voltage Quality in Low-Voltage Industrial Networks of Estonia” (T. Vinnal, K. Janson, et al., Estonian Journal of Engineering, 2012:102–126) presents voltage measurements for a sample of 66 industrial networks in Estonia. Assume the rated voltage for these networks is 232 V. The sample mean voltage was 231.7 V with a standard deviation of 2.19 V. Let μ represent the population mean voltage for these networks. a) Find the P-value for testing H0: μ = 232 versus H1: μ ≠ 232. b) Either the mean voltage is not equal to 232, or the sample is in the most extreme _____% of its distribution.Question

Asked Feb 21, 2020

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The article “Supply Voltage Quality in Low-Voltage Industrial Networks of Estonia” (T. Vinnal, K. Janson, et al., Estonian Journal of Engineering, 2012:102–126) presents voltage measurements for a sample of 66 industrial networks in Estonia. Assume the rated voltage for these networks is 232 V. The sample mean voltage was 231.7 V with a standard deviation of 2.19 V. Let μ represent the population mean voltage for these networks. a) Find the P-value for testing H_{0}: μ = 232 versus H_{1}: μ ≠ 232. b) Either the mean voltage is not equal to 232, or the sample is in the most extreme _____% of its distribution.

Step 1

**Note: here, MINITAB software is used to obtain the hypothesis test for proportion.**

** **

**a.**

In a sample of 50 batches, the mean pH was 2.6 with a standard deviation of 0.3.

*Tests statistic:*

**Software Procedure:**

Step-by-step procedure to obtain the test statistic using the MINITAB software:

- Choose
**Stat > Basic Statistics > 1-Sample**.*Z* - In
**Summarized data,**enter the**sample size as 50**and**mean**as**2.6**. - In
**Standard deviation**, enter a value for*s*as**0.3**. - In
**Perform hypothesis test,**enter the hypothesized mean as**2.5**. - Check
**Options**; enter**Confidence level**as**95%**. - Choose
**greater than**in**alternative**. - Click
**OK**.

Output using the MINITAB software is given below:

Step 2

From the MINITAB output, the test statistic is 2.36.

*P-value:*

**Software Procedure:**

Step-by-step procedure to obtain the *P-* value using the MINITAB software:

- Choose
**Graph > Probability Distribution Plot**choose**View Probability > OK.** - From
**Distribution**, choose ‘**Normal**’ distribution. - Click the
**Shaded Area**tab. - Choose
and*X*Value**Right Tail**for the region of the curve to shade. - Enter the
**data value**as**2.36**. - Click
**OK**.

Output using the MINIT...

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