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eimsori [14]
3 years ago
5

Determine whether the following sampling is dependent or independent. Indicate whether the response variable is qualitative or q

uantitative. A researcher wishes to compare academic aptitudes of married lawyers and their spouses. She obtains a random sample of 517 such couples who take an academic aptitude test and determines each spouse's academic aptitude.
Mathematics
1 answer:
sleet_krkn [62]3 years ago
3 0

Answer:

a) Independent

b) Quantitative  

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 517

Sample:

Married lawyers and their spouses.

Response variable:

Comparison of academic aptitudes of married lawyers and their spouses.

a) The given sampling is an example of independent sampling.

This is an independent sample because an individual of sample does not effect any other individual of the sample.

b) The response variable is academic aptitude. Since it is a numeric measure, it is a quantitative variable.

It is a quantitative measure because the scores can be expressed in numerical.

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Answer:

The minimum sample size that should be taken is 62.

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{1-0.9}{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

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.

If we want to be 90% confident that the sample mean is within 1 word per minute of the true population mean, what is the minimum sample size that should be taken

This is n when M = 1, \sigma = 4. So

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

1 = 1.96*\frac{4}{\sqrt{n}}

\sqrt{n} = 4*1.96

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

n = 61.5

The minimum sample size that should be taken is 62.

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3 years ago
Decide which item is the better purchase in the scenario below.
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The 3oz is better than the 20
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Decorations for a seventh-grade dance take 1/6 of the student council's budget. entertainment takes 3/8 of the budget. what frac
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11/24 is left over

Step-by-step explanation:

1/6 + 3/8 = 13/24

24/24 - 13/24 = 11/24

11/24 of the budget is left over

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30°<br> 8 + 6x<br> 4x + 2 <br> in a triangle
andrey2020 [161]

Answer:

x=12

Step-by-step explanation:

Simplifying

30 + 4x + 2 = 8 + 6x

Reorder the terms:

30 + 2 + 4x = 8 + 6x

Combine like terms: 30 + 2 = 32

32 + 4x = 8 + 6x

Solving

32 + 4x = 8 + 6x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-6x' to each side of the equation.

32 + 4x + -6x = 8 + 6x + -6x

Combine like terms: 4x + -6x = -2x

32 + -2x = 8 + 6x + -6x

Combine like terms: 6x + -6x = 0

32 + -2x = 8 + 0

32 + -2x = 8

Add '-32' to each side of the equation.

32 + -32 + -2x = 8 + -32

Combine like terms: 32 + -32 = 0

0 + -2x = 8 + -32

-2x = 8 + -32

Combine like terms: 8 + -32 = -24

-2x = -24

Divide each side by '-2'.

x = 12

Simplifying

x = 12

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