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Airida [17]
3 years ago
9

Brewed decaffeinated coffee contains some caffeine. We want to estimate the amount of caffeine in 8 ounce cups of decaf coffee a

t local fast food restaurants. Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg. If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result
Mathematics
1 answer:
rusak2 [61]3 years ago
8 0

Answer:

We would have to take a sample of 62 to achieve this result.

Step-by-step explanation:

Confidence level of 95%.

We have that to find our \alpha level, that is the subtraction of 1 by the confidence interval divided by 2. So:

\alpha = \frac{1 - 0.95}{2} = 0.025

Now, we have to find z in the Ztable as such z has a pvalue of 1 - \alpha.

That is z with a pvalue of 1 - 0.025 = 0.975, so Z = 1.96.

Now, find the margin of error M as such

M = z\frac{\sigma}{\sqrt{n}}

In which \sigma is the standard deviation of the population and n is the size of the sample.

Assume that the standard deviation in the amount of caffeine in 8 ounces of decaf coffee is known to be 2 mg.

This means that \sigma = 2

If we wanted to estimate the true mean amount of caffeine in 8 ounce cups of decaf coffee to within /- 0.5 mg, how large a sample would we have to take to achieve this result?

We would need a sample of n.

n is found when M = 0.5. So

M = z\frac{\sigma}{\sqrt{n}}

0.5 = 1.96\frac{2}{\sqrt{n}}

0.5\sqrt{n} = 2*1.96

Dividing both sides by 0.5

\sqrt{n} = 4*1.96

(\sqrt{n})^2 = (4*1.96)^2

n = 61.5

Rounding up

We would have to take a sample of 62 to achieve this result.

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The linearized regression equation for an exponential data set is log ŷ = 0.14x + 0.4, where x is the number of years and y is t
djyliett [7]

Option C: 316 is the predicted population when x=15

Explanation:

The regression equation for an exponential data is \log y=0.14x+0.4

Where x is the number of years and

y is the population

We need to determine the predicted population when x=15

The population x can be determined by substituting x=15 in the equation \log y=0.14x+0.4

Thus, we have,

\log y=0.14(15)+0.4

\log y=2.1+0.4

\log y=2.5

Using the logarithmic definition \log _{a}(b)=c then b=a^{c}

\log _{10}(y)=2.5 \Rightarrow y=10^{2.5}

y=316.22776 \ldots

Rounding off to the nearest whole number, we get,

y=316

Thus, the predicted population when x=15 is 316

Hence, Option C is the correct answer.

7 0
3 years ago
Pls help me its due sooon
stira [4]

Answer:

nobody

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Which expression is equivalent to (x – 1)7?
aleksley [76]
Hello!

The answer is B

Hope this helps!
6 0
3 years ago
CAN SOMEONE HELP ME PLS
Y_Kistochka [10]

Answer:

0.5 < x < 16.5

Step-by-step explanation:

8.5 - 8.0 < x < 8.5 + 8.0 =

0.5 < x < 16.5

<em>Hope that helps! :)</em>

<em></em>

<em>-Aphrodite</em>

8 0
3 years ago
Answer ASAP 84.9 66.2 38.2 33.8
tankabanditka [31]

Step-by-step explanation:

You need to use trigonometric stuff here. Since you're given the hypotenuse and an angle you can plug that right into an equation.

Recall that sin is opposite over hypotenuse and cos is adjacent over hypotenuse.

sin(\theta)=\frac{o}{h} \\sin(30)=\frac{x}{14} \\0.5=\frac{x}{14} \\x=7

Now that you know the opposite side (DC) you can use tan, too, but I'm going to use cos.

cos(\theta)=\frac{a}{14} \\cos(30)=\frac{x}{14} \\\frac{\sqrt{3} }{2} =\frac{x}{14} \\x=7\sqrt{3}

This is the adjacent side (BC). I put it in its exact value, but in decimal form it's ≈12.124.

Now you can do the perimeter:

2l+2w\\2(12.124)+2(7)\\24.248+14\\38.25

Your answer is the 38.2

6 0
3 years ago
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