An article 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 231.5 V with a standard deviation of 2.19 V. Let μ represent the population mean voltage for these networks. Find the P-value for testing H0 : μ = 232 versus H1 : µ ≠ 232. Round the answer to four decimal places.

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ChiKesselman ChiKesselman · Answer 1 · 2019-11-05T09:17:36+01:00

Answer:

We accept the null hypothesis and conclude that voltage for these networks is 232 V.

Step-by-step explanation:

We are given the following in the question:

Population mean, μ = 232 V

Sample mean, [tex]\bar{x}[/tex] = 231.5 V

Sample size, n = 66

Sample standard deviation, s = 2.19 V

Alpha, α = 0.05

First, we design the null and the alternate hypothesis

[tex]H_{0}: \mu = 232\\H_A: \mu \neq 232[/tex]

We use Two-tailed t test to perform this hypothesis.

Formula:

[tex]t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n-1}} }[/tex] Putting all the values, we have

[tex]t_{stat} = \displaystyle\frac{231.5- 232}{\frac{2.19}{\sqrt{66}} } = -1.8548[/tex]

Now,

[tex]t_{critical} \text{ at 0.05 level of significance, 9 degree of freedom } = \pm 1.9971[/tex]

Since,

[tex]|t_{stat}| > |t_{critical}|[/tex]

We accept the null hypothesis and conclude that voltage for these networks is 232 V.