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ycow [4]
3 years ago
7

Of a group of randomly selected adults, 360 identified themselves as manual laborers, 280 identified themselves as non-manual wa

ge earners, 250 identified themselves as mid-level managers, and 160 identified themselves as executives. In the survey, 295 of manual laborers preferred trucks, 174 of non-manual wage earners preferred trucks, 135 of mid-level managers preferred trucks, and 42 of executives preferred trucks. We are interested in finding the 95% confidence interval for the percent of executives who prefer trucks.
Which distribution should you use for this problem?

Construct a 95% confidence interval.

State the confidence interval and interpret this result in regards to the context of the problem.
Mathematics
1 answer:
Wittaler [7]3 years ago
5 0

Answer:

We are 95% confident that the percent of executives who prefer trucks is between 19.43% and 33.06%

Step-by-step explanation:

We are given that in a group of randomly selected adults, 160 identified themselves as executives.

n = 160

Also we are given that 42 of executives preferred trucks.

So the proportion of executives who prefer trucks is given by

p = 42/160

p = 0.2625

We are asked to find the 95% confidence interval for the percent of executives who prefer trucks.

We can use normal distribution for this problem if the following conditions are satisfied.

n×p ≥ 10

160×0.2625 ≥ 10

42 ≥ 10 (satisfied)

n×(1 - p) ≥ 10

160×(1 - 0.2625) ≥ 10

118 ≥ 10 (satisfied)

The required confidence interval is given by

$ p \pm z\times \sqrt{\frac{p(1-p)}{n} } $

Where p is the proportion of executives who prefer trucks, n is the number of executives and z is the z-score corresponding to the confidence level of 95%.

Form the z-table, the z-score corresponding to the confidence level of 95% is 1.96

$ p \pm z\times \sqrt{\frac{p(1-p)}{n} } $

$ 0.2625 \pm 1.96\times \sqrt{\frac{0.2625(1-0.2625)}{160} } $

$ 0.2625 \pm 1.96\times 0.03478 $

$ 0.2625 \pm 0.06816 $

0.2625 - 0.06816, \: 0.2625 + 0.06816

(0.1943, \: 0.3306)

(19.43\%, \: 33.06\%)

Therefore, we are 95% confident that the percent of executives who prefer trucks is between 19.43% and 33.06%

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KATRIN_1 [288]

Answer:

See Explanation

Step-by-step explanation:

Given

Ratio=12:40

Required

Determine the actual distance between x and y

The question is incomplete, as the scale distance between x and y is not given.

To solve this, we make assumptions.

A scale measurement is represented as:

Ratio =  Scale : Actual

So, we have:

Scale : Actual = 12 : 40

Express as fraction

\frac{Actual}{Scale} = \frac{40}{12}

Make Actual, the subject

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Now, assume that the distance between x and y is 60 (on the scale), the actual distance traveled will be:

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2 years ago
Which statement is true about ∠JXM and ∠NXP? a.∠JXM and ∠NXP are complementary. b.∠JXM and ∠NXP are vertical. c.∠JXM and ∠NXP ar
xenn [34]

Answer:

Incomplete questions

Check attachment for correct question.

The correct answer is

A. ∠JXM and ∠NXP are complementary

step explanation:

line JP is a straight line and sum of angle on a straight line is 180°.

There are three angles on this straight line JP which are ∠JXM, ∠NXP and ∠MXN

Note: from the attachment, it is shown that ∠MXN is a right angle i.e. 90°.

Then, sum of angle on this line is 180°.

∠JXM + ∠NXP + ∠MXN = 180°

∠JXM + ∠NXP + 90° = 180°

∠JXM + ∠NXP = 180° — 90°

∠JXM + ∠NXP = 90°

From the definition of complementary angles : Two Angles are said to Complementary if their sum is 90° (a Right Angle).

They don't have to be next to each other, just so long as the sum is 90 degrees.

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3 years ago
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Stella [2.4K]

Answer:

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Step-by-step explanation:

Let, the price of the pencil is $ .

Given that the pen costs a dollar more than the pencil,

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, =0.10/2

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The pencil cost $0.05 and the pen cost $1.05.

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g100num [7]

Answer:

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Step-by-step explanation:

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Verdich [7]

Answer:The answer is Equal.

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