Question

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.

Answer 1

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

Explanation:

We are given the following in the question:

Population mean, μ = 232 V

Sample mean,
`\bar{x}` = 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

`H_(0): \mu = 232\\H_A: \mu \\eq 232`

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

Formula:

`t_(stat) = \displaystyle\frac{\bar{x} - \mu}{(\sigma)/(√(n-1)) }` Putting all the values, we have

`t_(stat) = \displaystyle(231.5- 232)/((2.19)/(√(66)) ) = -1.8548`

Now,

`t_(critical) \text{ at 0.05 level of significance, 9 degree of freedom } = \pm 1.9971`

Since,

`|t_(stat)| > |t_(critical)|`

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