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ollegr [7]
4 years ago
12

A researcher selects a random sample of 500 college students from Kentucky. It is found that 23% of students in the sample are s

cience majors. The actual percentage of Kentucky college students that are science majors is 26%. Which type of error explains this discrepancy?
Mathematics
2 answers:
balu736 [363]4 years ago
8 0

Answer:

Sampling error is the answer.

Step-by-step explanation:

A researcher selects a random sample of 500 college students from Kentucky.

It is found that 23% of students in the sample are science majors but the actual percentage of Kentucky college students that are science majors is 26%.

This depicts sampling error in collecting data.

Sampling error is the reason for the difference between an estimate and the actual value of the population parameter. This error is caused by observing a sample instead of the whole population.

forsale [732]4 years ago
6 0
The type of error which explains this discrepancy is the sampling error. Sampling error is defined as an error caused by using or utilizing a number of samples instead of using the entire population number. In this case, the error came from the 500 Kentucky college students instead of using all Kentucky college students. 
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The following results come from two independent random samples taken of two populations.
photoshop1234 [79]

Answer:

(a)\ \bar x_1 - \bar x_2 = 2.0

(b)\ CI =(1.0542,2.9458)

(c)\ CI = (0.8730,2.1270)

Step-by-step explanation:

Given

n_1 = 60     n_2 = 35      

\bar x_1 = 13.6    \bar x_2 = 11.6    

\sigma_1 = 2.1     \sigma_2 = 3

Solving (a): Point estimate of difference of mean

This is calculated as: \bar x_1 - \bar x_2

\bar x_1 - \bar x_2 = 13.6 - 11.6

\bar x_1 - \bar x_2 = 2.0

Solving (b): 90% confidence interval

We have:

c = 90\%

c = 0.90

Confidence level is: 1 - \alpha

1 - \alpha = c

1 - \alpha = 0.90

\alpha = 0.10

Calculate z_{\alpha/2}

z_{\alpha/2} = z_{0.10/2}

z_{\alpha/2} = z_{0.05}

The z score is:

z_{\alpha/2} = z_{0.05} =1.645

The endpoints of the confidence level is:

(\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}

2.0 \± 1.645 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}

2.0 \± 1.645 * \sqrt{\frac{4.41}{60}+\frac{9}{35}}

2.0 \± 1.645 * \sqrt{0.0735+0.2571}

2.0 \± 1.645 * \sqrt{0.3306}

2.0 \± 0.9458

Split

(2.0 - 0.9458) \to (2.0 + 0.9458)

(1.0542) \to (2.9458)

Hence, the 90% confidence interval is:

CI =(1.0542,2.9458)

Solving (c): 95% confidence interval

We have:

c = 95\%

c = 0.95

Confidence level is: 1 - \alpha

1 - \alpha = c

1 - \alpha = 0.95

\alpha = 0.05

Calculate z_{\alpha/2}

z_{\alpha/2} = z_{0.05/2}

z_{\alpha/2} = z_{0.025}

The z score is:

z_{\alpha/2} = z_{0.025} =1.96

The endpoints of the confidence level is:

(\bar x_1 - \bar x_2) \± z_{\alpha/2} * \sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}

2.0 \± 1.96 * \sqrt{\frac{2.1^2}{60}+\frac{3^2}{35}}

2.0 \± 1.96* \sqrt{\frac{4.41}{60}+\frac{9}{35}}

2.0 \± 1.96 * \sqrt{0.0735+0.2571}

2.0 \± 1.96* \sqrt{0.3306}

2.0 \± 1.1270

Split

(2.0 - 1.1270) \to (2.0 + 1.1270)

(0.8730) \to (2.1270)

Hence, the 95% confidence interval is:

CI = (0.8730,2.1270)

8 0
4 years ago
The angle of elevation from a point on the ground to the top of a pyramid is 31 degrees 10​' The angle of elevation from a point
mart [117]

Answer:

h ≈ 209 ft

Step-by-step explanation:

The illustration forms 2 right angle triangle with same height , which is the height of the pyramid.

The first triangle has an unknown adjacent side and height but the angle is 31° 10'. The larger triangle has adjacent side of 120 ft plus the adjacent side of the smaller triangle.

let

the adjacent side of the smaller triangle = a

recall both triangle have same height = h

Therefore,

tan 31° 10' = opposite/adjacent = h/a

tan 31.167 = h/a

h = a tan 31.167

h = 0.6048345941  a

The larger triangle

adjacent side = 120 + a

height = h

tan 24° 10' = h/120 + a

convert the minutes to degree

tan 24.167° = h/120 + a

cross multiply

120 + a tan 24.167 = h

120 + a (0.44872570999 ) = h

h = 53.8470851998  + 0.44872570999a

Therefore,

0.6048345941  a  = 53.8470851998  + 0.44872570999a

0.6048345941  a  - 0.44872570999a = 53.8470851998

0.1561094942 a = 53.8470851998

divide both sides by 0.1561094942

a = 53.8470851998 / 0.1561094942

a = 344.931520506

a ≈ 345 ft

The height can be computed as

tan 31.167 = h/a

h = 345 × tan 31.167

h = 345 × 0.6048345941

h = 208.667934967

h ≈ 209 ft

6 0
4 years ago
Please answer this and will marked as brainlist ​
xeze [42]
<h3>Answer: 1</h3>

where x is nonzero

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

Explanation:

We'll use two rules here

  • (a^b)^c = a^(b*c) ... multiply exponents
  • a^b*a^c = a^(b+c) ... add exponents

------------------------------

The portion [ x^(a-b) ]^(a+b) would turn into x^[ (a-b)(a+b) ] after using the first rule shown above. That turns into x^(a^2 - b^2) after using the difference of squares rule.

Similarly, the second portion turns into x^(b^2-c^2) and the third part becomes x^(c^2-a^2)

-------------------------------

After applying rule 1 to each of the three pieces, we will have 3 bases of x with the exponents of (a^2-b^2),  (b^2-c^2) and (c^2-a^2)

Add up those exponents (using rule 2 above) and we get

(a^2-b^2)+(b^2-c^2)+(c^2-a^2)

a^2-b^2+b^2-c^2+c^2-a^2

(a^2-a^2) + (-b^2+b^2) + (-c^2+c^2)

0a^2 + 0b^2 + 0c^2

0+0+0

0

All three exponents add to 0. As long as x is nonzero, then x^0 = 1

4 0
3 years ago
Given -10x-2y=16 prove y=-5x-8
irga5000 [103]

Answer:

y doesn't equal -5x-8

Step-by-step explanation:

-10x - 2 (-5x-8) = 16

-10x + 10x +32 =16

32=16? wrong

7 0
3 years ago
Kendall's sister is 156 months old. Kendall is 3 years older than her sister. How many years old is Kendall?
Lena [83]
Kendall is 16 you do 156/12 and you get 13 then add 3 and you get 16
4 0
4 years ago
Read 2 more answers
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