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Ad libitum [116K]
3 years ago
12

A researcher wants to estimate the mean age of all Business Week readers at a 99% confidence level. The standard deviation of ag

es of all Business Week readors is nine years. The sample size that will yield a maximum error of estimate within three years of the population mean is at least:
A. 60
B. 97
C. 185
D. 8
Mathematics
1 answer:
Natasha2012 [34]3 years ago
5 0

Answer:

A. 60

Step-by-step explanation:

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

\alpha = \frac{1-0.99}{2} = 0.005

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

So it is z with a pvalue of 1-0.005 = 0.995, so z = 2.575

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.

We have to find:

n when M = 3, \sigma = 9. So

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

3 = 2.575*\frac{9}{\sqrt{n}}

3\sqrt{n} = 9*2.575

Dividing both sides by 3

\sqrt{n} = 3*2.575

(\sqrt{n})^{2} = (3*2.575)^{2}

n = 59.68

We round up, so the correct answer is:

A. 60

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(5x10^7)(6x10^4) in scientific notation
Ratling [72]

Answer:

(5 x 10^7)(6 x 10^4)= 3 x 10^12 is the answer in scientific notation

Step-by-step explanation:

5 0
3 years ago
Based on the given information, what can you conclude and why
Dmitry_Shevchenko [17]
Notice the point R
is a vertex between two "vertical angles" \measuredangle SRT\ and\ \measuredangle QRP

those two folks are also the same
so now, we have the left triangle has angle P equals to angle T on the other triangle
we also have the side on the left triangle of PR equals the side of TR on the other triangle, and those two verticals angles are equal to each other

does ASA ring a bell?
8 0
3 years ago
Joe has read ​30 % of a book. He has 63 more pages to finish. How many pages are there in the​ book?
meriva

Answer:

90 pages

Step-by-step explanation:

30% complete

70% to go = 63 pages

t = total number of pages

0.7t = 63

∴ t = ⁶³/₀.₇

⁶³/₀.₇ = 90

4 0
3 years ago
There are 2,000 eligible voters in a precinct. A total of 500 voters are randomly selected and asked whether they plan to vote f
Ann [662]

Answer:

0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647

0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

p \sim N(p,\sqrt{\frac{p(1-p)}{n}})

Solution to the problem

The estimated population proportion for this case is:

\hat p = \frac{350}{500}=0.7

The confidence interval would be given by this formula

\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}

For the 99% confidence interval the value of \alpha=1-0.99=0.01 and \alpha/2=0.005, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=2.58

And replacing into the confidence interval formula we got:

0.7 - 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.647

0.7 + 2.58 \sqrt{\frac{0.7(1-0.7)}{500}}=0.753

And the 99% confidence interval would be given (0.647;0.753).

So the correct answer would be:

a. 0.647 and 0.753

7 0
3 years ago
Round 9.77 to the nearest tenth
djyliett [7]
9.77 to the nearest tenths

first, find the number that is in the tenths place....it is 7....now look at the number directly to the right of it....if that number is 5 or greater, u would round that 7 up to an 8...but if that number is 4 or below, ur 7 would stay the same.
So the number directly to the right of 7 is 7...and since it is greater then 5, u have to round the 7 in the tenths place up to 8.

solution is : 9.8
3 0
3 years ago
Read 2 more answers
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