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2 answers:
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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:
1) Let's consider the first case with the number 0 the oppose is also 0 and we have that 0-0=0 so then applies
2) Now let's consider any real number a no matter positive or negative we will have that:
Or in the other case:
So then we can conclude that the expression is a general rule and is true
Step-by-step explanation:
For this case we can verify if the following expression is true or false:
The sum of x and it’s opposite is always zero?
If we want to proof this we need to show that for any number is true.
1) Let's consider the first case with the number 0 the oppose is also 0 and we have that 0-0=0 so then applies
2) Now let's consider any real number a no matter positive or negative we will have that:
Or in the other case:
So then we can conclude that the expression is a general rule and is true