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3 years ago

14

Suppose we take two different random samples from the same population of test scores. The population mean and standard deviation

are unknown. The first sample has 25 data values. The second sample has 64 data values. Then we construct a 95% confidence interval for each sample to estimate the population mean. Which confidence interval will have greater precision (smaller width) for estimating the population mean?

1 answer:

Leto [7]3 years ago

3 0

Answer:

The 95% confidence interval obtained with a sample size of 64 will give greater precision.

Step-by-step explanation:

We are given the following in the question:

A 95% confidence interval is calculated with the following sample sizes

$n_1 = 25\\n_2 = 64$

The population mean and standard deviation are unknown.

Effect of sample size on confidence interval:

As the sample size increases the margin of error decreases.
As the margin of error decreases the width of the confidence level decreases.
Thus, with increased sample size the width of confidence level decreases.

If we want a confidence interval with greater precision that is smaller width, we have to choose the higher sample size.

Thus, the 95% confidence interval obtained with a sample size of 64 will give greater precision.

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A supervisor finds the mean number of miles that the employees in a department live from work. Which mileage is within a z-score

Vikentia [17]

The z-score tells you how many standard deviations from the mean.

<span>1.5 * 3.6 = 5.4 miles </span>

<span>So anything within 5.4 miles of the average (29). </span>

<span>The range would be: </span>
<span>29 - 5.4 = 23.6 </span>
<span>to: </span>
<span>29 + 5.4 = 34.4 </span>

<span>23.6 ≤ x ≤ 34.4 </span>

<span>Answer: </span>
<span>B) 24 miles</span>

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3 years ago

Read 2 more answers

19) Two of the dozen eggs in a carton are cracked. About what percent of the carton is not cracked? (Round to the nearest whole

777dan777 [17]

Answer:

$83%$ %

Step-by-step explanation:

We have that $2/12=1/6$ of the eggs are cracked, so $1-1/6=5/6$ of the eggs are not cracked.

Recall that $1/6=0.1666666666...$ . This means that $5/6=1-1/6=1-0.166666666...=0.833333333...$ .

Rounding this to the nearest whole percent gives $83%$ %.

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3 years ago

10. Simplify the rational expression by rationalizing the denominator. 3 sqrt 160/sqrt 1350x A) 2 sqrt 15x/15x B) 3 sqrt 160/135

Viefleur [7K]

The simplified expression by rationalizing the denominator is (C) $\frac{4 \sqrt{15x} }{15x}$ .

First we must simplify the expression:
$\frac{3 \sqrt{160} }{\sqrt{1350x} } = \frac{12 \sqrt{10} }{15 \sqrt{6x} } = \frac{4 \sqrt{10} }{5 \sqrt{6x} }$

Then we factor the rational parts and cancel it out:
$\frac{4 \sqrt{2} \sqrt{5} }{5 \sqrt{2} \sqrt{3x} } = \frac{4\sqrt{5} }{5\sqrt{3x} }$

Then we rationalize the expression:
$\frac{4\sqrt{5} }{5\sqrt{3x} } * \frac{\sqrt{3x} }{\sqrt{3x} } = \frac{4 \sqrt{15x} }{5*3x} = \frac{4 \sqrt{15x} }{15x}$

<span>Finally, the simplified expression by rationalizing the denominator is (C) $\frac{4 \sqrt{15x} }{15x}$ .</span>

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3 years ago

A water tank is 3/4 full.

guapka [62]

x/.75=x-56/0.4

0.4x=.75x-42

-0.35x=-42

x=120

I set up a proportion in which x=the tank when it is 3/4 full. When the tank is 3/4 full, solving the proportion tells us the x=120 litres. 120/3=40, and 120+40 is 160, showing that a tank completely full would indeed hold 160 litres.

Hope this helps!

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3 years ago

In a rational function, is the horizontal shift represented by the vertical asymptote?

ziro4ka [17]

<h3>Short Answer: Yes, the horizontal shift is represented by the vertical asymptote</h3>

A bit of further explanation:

The parent function is y = 1/x which is a hyperbola that has a vertical asymptote overlapping the y axis perfectly. Its vertical asymptote is x = 0 as we cannot divide by zero. If x = 0 then 1/0 is undefined.

Shifting the function h units to the right (h is some positive number), then we end up with 1/(x-h) and we see that x = h leads to the denominator being zero. So the vertical asymptote is x = h

For example, if we shifted the parent function 2 units to the right then we have 1/x turn into 1/(x-2). The vertical asymptote goes from x = 0 to x = 2. This shows how the vertical asymptote is very closely related to the horizontal shifting.

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3 years ago