Jared is going to plant 20 small plants around the edge of a circular garden that is 8 feet in diameter. If he spaces the plants
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Answer:
(a) Null Hypothesis, :
3.50 mg
Alternate Hypothesis, :
> 3.50 mg
(b) The value of z test statistics is 2.50.
(c) We conclude that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg.
(d) The p-value is 0.0062.
Step-by-step explanation:
We are given that Green Beam Ltd. claims that its compact fluorescent bulbs average no more than 3.50 mg of mercury. A sample of 25 bulbs shows a mean of 3.59 mg of mercury. Assuming a known standard deviation of 0.18 mg.
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<u><em>Let </em></u><u><em> = average mg of mercury in compact fluorescent bulbs.</em></u>
So, Null Hypothesis, :
3.50 mg {means that the average mg of mercury in compact fluorescent bulbs is no more than 3.50 mg}
Alternate Hypothesis, :
> 3.50 mg {means that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg}
The test statistics that would be used here <u>One-sample z test</u> <u>statistics</u> as we know about the population standard deviation;
T.S. = ~ N(0,1)
where, = sample mean mg of mercury = 3.59
= population standard deviation = 0.18 mg
n = sample of bulbs = 25
So, <em><u>test statistics</u></em> =
= 2.50
The value of z test statistics is 2.50.
<u>Now, P-value of the test statistics is given by;</u>
P-value = P(Z > 2.50) = 1 - P(Z 2.50)
= 1 - 0.9938 = 0.0062
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<em>Now, at 0.01 significance level the z table gives critical value of 2.3263 for right-tailed test. Since our test statistics is more than the critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><em><u>we reject our null hypothesis</u></em><em>.</em>
Therefore, we conclude that the average mg of mercury in compact fluorescent bulbs is more than 3.50 mg.
Answer:
Step-by-step explanation:
Left
As near as I can tell, the question is x^(1/2) * x^(1/2) = The bases are the same, so all you do is add the powers.
x^(1/2 + 1/2) = x^1 which is just x.
Right
The is another one where the work is hard to show. The numerator (m) of the fraction is the power and the denominator (n) is the root. That sentence is all the work there is.
So you would write