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PtichkaEL [24]
3 years ago
15

Use emilimination to solve 2t 3n=9 and 5t-3n=5

Mathematics
1 answer:
Vladimir [108]3 years ago
3 0
2t+3n=9                                                   2(2)+3n=9
+5t-3n=5 (the 3n cancel out)                   4+3n=9
7t=14                                                       3n=5
t=2                                                           n=5/3 or 1.67
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Part A

Given info:

  • xbar = sample mean = 4.90 ppm
  • s = sample standard deviation = 1.12 ppm
  • n = 23 = sample size

Because n > 30 is not true, and we don't know the population standard deviation (sigma), this means we must use a T distribution.

The degrees of freedom here are n-1 = 23-1 = 22.

At 90% confidence and the degrees of freedom mentioned, the t critical value is roughly t = 1.717

Use a T distribution table or calculator to determine this. If you don't have a calculator for the task, then you can search out "inverse T calculator" and there are tons of free options to pick from.

The margin of error E is

E = t*s/sqrt(n)

E = 1.717*1.12/sqrt(23)

E = 0.400982

This is approximate and accurate to 6 decimal places.

The confidence interval is going to be xbar plus or minus that E value

L = lower bound = xbar - E = 4.90 - 0.400982 = 4.499018 = 4.50

U = upper bound = xbar + E = 4.90 + 0.400982 = 5.300982 = 5.30

The confidence interval in the format of (L, U) is (4.50, 5.30)

You could also express it as the format L < mu < U and it would be 4.50 < mu < 5.30; however, I'll stick to the first method.

<h3>Answer:  (4.50, 5.30)</h3>

=====================================================

Part B

Since we know sigma = 2.6 is the population standard deviation, we can use a Z distribution now.

At 90% confidence, the z critical value is roughly 1.645; use a table or calculator to determine this.

n = \left(\frac{z*\sigma}{E}\right)^2\\\\n \approx \left(\frac{1.645*2.6}{0.03}\right)^2\\\\n \approx 20325.254444 \\\\

Round this up to the nearest integer to get 20326. For min sample size problems, <u>always</u> round up.

<h3>Answer: 20326</h3>
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