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tekilochka [14]

3 years ago

14

Michael gave 2/5 of his marbles to his sister. He then divided the remainder equally among his 3 friends. If each of his friends

receives 12 marbles, how many marbles did Michael have at first?

1 answer:

eduard3 years ago

3 0

He had 50 marbles at first

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2 years ago

An article presents voltage measurements for a sample of 66 industrial networks in Estonia. Assume the rated voltage for these n

kramer

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, $\bar{x}$ = 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

$H_{0}: \mu = 232\\H_A: \mu \neq 232$

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

Formula:

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

$t_{stat} = \displaystyle\frac{231.5- 232}{\frac{2.19}{\sqrt{66}} } = -1.8548$

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.

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2 years ago