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aliina [53]
3 years ago
7

25 scores from all of the students who took the test. She sees that the mean score is 134 with a standard deviation of 6.0547. T

he superintendant wants to know if the standard deviation has changed this year. Previously, the population standard deviation was 13. Is there evidence that the standard deviation of test scores has decreas
Mathematics
1 answer:
Tomtit [17]3 years ago
7 0

Answer:

WE fail to reject the Null and conclude that ; Standard deviation of test hasn't decreased.

Step-by-step explanation:

The hypothesis :

H0 : σ = 13

H1 : σ < 13

Using the Chisquare Square statistic :

χ² = (n-1)*s²/σ²

Sample size, n = 25

s² = 6.0547²

σ² = 13²

χ² = (25 - 1)*6.0547² / 13²

χ² = 879.82541016 / 169

χ² = 5.206

The degree of freedom, df = 25 - 1 = 24

The Pvalue(5.206, 24) = 0.99981

Reject H0, if Pvalue < α ;

Since Pvalue > α ; WE fail to reject the Null and conclude that ; Standard deviation of test hasn't decreased.

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Benjamin is trying to find the height of a radio antenna on the roof of a local building.
xz_007 [3.2K]

The height of the antenna on the roof of the local building is approximately 8 meters.

The situation forms a right angle triangle.

<h3>Properties of a right angle triangle:</h3>
  • One of its angles is equals to 90 degrees
  • The sides of the triangles can be calculated using Pythagoras theorem.

Therefore, let's find the height of the building and the radio antenna from the eye point.

Using trigonometric ratios,

tan 40° = opposite / adjacent

tan 40° = x / 25

where

x = the height of the building and the radio antenna from the eye point.

x = 25 tan 40

x = 25 × 0.83909963117

x = 20.9774907794 meters

Let's find the height of the building from his eye point.

tan 28° = y / 25

where

y = height of the building from his eye point

y = 25 × tan 28°

y = 25 × 0.53170943166

y = 13.2927357915 meters

Height of the antenna = 20.9774907794 - 13.2927357915 = 7.68475498786

Height of the antenna ≈ 8 meters

learn more on elevation here: brainly.com/question/17582385?referrer=searchResults

8 0
3 years ago
ΔABC is dilated by a scale factor of 0.25 with the origin as the center of dilation, resulting in the image ΔA′B′C′. If A = (-1,
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Answer:

  c.  d = 5

Step-by-step explanation:

The difference in coordinates B and C is (14, 17) -(2, 1) = (12, 16). When the figure is scaled by 0.25, that difference becomes ...

  0.25(12, 16) = (3, 4)

The length of a line segment with those coordinate differences is ...

  d = √(3² +4²) = √25 = 5 . . . . matches selection c.

3 0
3 years ago
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