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alexandr1967 [171]
3 years ago
12

Suppose we have a set of paired data, and let d = xafter − xbefore . The null hypothesis is H0 : μd = 0, the alternative hypothe

sis is Ha : μd ≠ 0, and the population standard deviation σ is not known. Jordan collects a sample of size n = 9 and computes d¯= 2.2 and sd = 3.3A) What is the value of the test statistic?B) The probability of obtaining a test statistic greater than Jordan's test statistic is 0.0403. Use this probability to determine the P-value for Jordan's hypothesis test. (Round to three decimal places.)
Mathematics
1 answer:
Sergio039 [100]3 years ago
7 0

Answer:

(a) The value of the test statistic is, <em>t</em> = 2.

(b) The <em>p</em>-value of the test is 0.081.

Step-by-step explanation:

The hypothesis for the paired difference test is:

H₀: \mu_{d}=0 vs. Hₐ: \mu_{d}\neq 0

<u>Given</u>:

\bar d=2.2\\SD_{d}=3.3\\n=9

(a)

The test statistic is:

t=\frac{\bar d}{\frac{SD_{d}}{\sqrt{n}} } \\=\frac{2.2}{\frac{3.3}{\sqrt{9}} }\\=2

The value of the test statistic is, <em>t</em> = 2.

(b)

It is provided that the P(T>2)=0.0403.

But the hypothesis test is two-tailed.

The <em>p</em>-value for the two-tailed test is:

p-value=2P(t>2) or p-value=2P(t

The <em>p</em>-value is:

p-value=2P(t>2)=2\times0.0403=0.0806\approx0.081

Thus, the <em>p</em>-value of the test is 0.081.

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A chemist examines 12 sedimentary samples for bromide concentraction. The mean bromide concentration for the sample date is 0.43
Umnica [9.8K]

Answer:

a) z = 1.645

b) Lower endpoint: 0.422cc/m³

Upper endpoint: 0.452 cc/m³

Step-by-step explanation:

Population is approximately normal, so we can find the normal confidence interval.

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

\alpha = \frac{1-0.9}{2} = 0.05

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 1-0.05 = 0.95, so z = 1.645. This is the critical value, the answer for a).

Now, find M as such

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

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M = 1.645*\frac{0.0325}{\sqrt{12}} = 0.015

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The upper end of the interval is the sample mean added to M. So it is 0.437 + 0.015 = 0.452 cc/m³.

b)

Lower endpoint: 0.422cc/m³

Upper endpoint: 0.452 cc/m³

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3 years ago
Vladimir says that the equation of the line that passes through points (negative 5, negative 3) and (10, 9) is y = four-fifths x
love history [14]

Answer:

Vladimir and Robyn both are correct.

Step-by-step explanation:

Let us check whether the points (-5,-3) and (10,9) are on the line y = \frac{4}{5}x + 1 or not.

The equation of the straight line passing through the given points (-5,-3) ans (10,9) is \frac{y - 9}{9 + 3} = \frac{x - 10}{10 + 5}

⇒ 5(y - 9) = 4(x - 10)

⇒ 5y = 4x + 5

⇒  y = \frac{4}{5}x + 1 .............. (1)

So, Vladimir is correct.

Now, Robyn says that the line passes through the points (-10,-7) and (-15,-11).

Then, both of the points satisfy the equation (1).

Therefore, Vladimir and Robyn both are correct. (Answer)

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