Answer:
Let us consider the expression:
(1)
Now, the quotient of power rules says that the numbers that have same base can be find by subtracting if powers are with same sign
And adding if powers are with opposite sign.
We will solve equation (1) by this quotient of power rule.
So, it can be rewritten as:
.
Answer:
Step-by-step explanation:
Hello!
You need to test if the true mean of the voltage of Estonian networks is 232.
You are given a sample of n= 66 industrial networks, with sample mean X[bar]= 231.7 V and standard deviation S= 2.19 V.
With the study variable X: "voltage of an Estonian industrial network" of unknown distribution, but a large enough sample, I'll apply the Central Limit Theorem and approximate the distribution of the sample mean to normal. Remember: Since the population mean is a paramenter of the normal distribution, you need to work under it.
H₀: μ = 232
H₁: μ ≠ 232
α: 0.05 (you were given no significance level, that's why I choose to use the most common one for the test)
Z= <u>X[bar] - μ </u>≈ N (0;1)
S/√n
Z= <u>X[bar] - μ </u>= <u> 231.7 - 232 </u> = -1.113
S/√n 2.19/√66
= -1.113
This test is two tailed, and so is the p-value, in other words, you have to take into account that the p-value is divided in the two tails.
Remember: The p-value is defined as the probability corresponding to the calculated statistic if possible under the null hypothesis (i.e. the probability of obtaining a value as extreme as the value of the statistic under the null hypothesis).
P(Z<-1.113) + P(Z>1.113) = P(Z<-1.113) + (1 - P(Z< 1.113)) = 0.1335 + (1 - 0.8665) = 0.267
p-value: 0.267
Comparing it to α: 0.05, the decision is to not reject the null hypothesis.
I hope it helps!