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marin [14]
3 years ago
12

You claim you are psychic and can predict a coin flip 60% of the time. To test your claim, your friend has you predict a coin fl

ip and then records whether or not you are correct. You do this 200 times and find you are right 135 times. Considering a null hypothesis that you are correctly predict the coin flip 60% of the time, using a hypothesis test, which of the following statements is most accurate?
a. You cannot reject the null at the 10% level of significance.
b. You can reject the null at the 10% level of significance, but cannot reject the null at the 5%, 2%, or 1% level of significance.
c. You can reject the null at the 10% and 5% level of significance, but cannot reject the null at the 2%, or 1% level of significance.
d. You can reject the null at the 10%, 5%, and 2% level of significance, but cannot reject the null at the 1% level of significance.
e. You can reject the null at the 10%, 5%, 2%, and 1% level of significance
Mathematics
1 answer:
Salsk061 [2.6K]3 years ago
5 0

Answer:

You can reject the null at the 10% and 5% level of significance, but cannot reject the null at the 2%, or 1% level of significance. ( D )

Step-by-step explanation:

let : P = 0.6

x = 135 , n = 200

<em>p </em>= 135 / 200 = 0.675

H0 : P = 0.6

Ha : P ≠ 0.6

performing the test statistic = ( 0.675 - 0.6 ) / \sqrt{\frac{0.60(1-0.60)}{200} }

= 0.075 / 0.0346 ≈ 2.17

p-value = 2 * P ( Z > - 2.17 )  ( using excel function ; NORMSDIST )

            = 2 * 0.015  = 0.03  

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Select all the conditions for which it is possible to construct a triangle. (7.G.1.2) Group of answer choices a. A triangle with
saw5 [17]

Answer:

  b, d, e, f

Step-by-step explanation:

Here are the applicable restrictions:

  • The sum of angles in a triangle is 180°, no more, no less.
  • The sum of the lengths of the two shortest sides exceeds the longest side.
  • When two sides and the angle opposite the shortest is given, the sine of the given angle must be at most the ratio of the shortest to longest sides.

a. A triangle with angle measures 60°, 80°, and 80° (angle sum ≠ 180°, not OK)

b. A triangle with side lengths 4 cm, 5 cm, and 6 cm (4+5 > 6, OK)

c. A triangle with side lengths 4 cm, 5 cm, and 15 cm (4+5 < 15, not OK)

d. A triangle with side lengths 4 cm, 5 cm, and a 50° angle across from the 4 cm side (sin(50°) ≈ 0.766 < 4/5, OK)

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_____

<em>Additional comment</em>

In choice "e", two angles and the side between them are specified. As long as the sum of the two angles is less than 180°, a triangle can be formed. The length of the side is immaterial with respect to whether a triangle can be made.

__

The congruence postulates for triangles are ...

  SSS, SAS, ASA, AAS, and HL

These essentially tell you the side and angle specifications necessary to define <em>a singular triangle</em>. As we discussed above, the triangle inequality puts limits on the side lengths specified in SSS. The angle sum theorem puts limits on the angles when only two are specified (ASA, AAS).

In terms of sides and angles, the HL postulate is equivalent to an SSA theorem, where the angle is 90°. In that case, the angle is opposite the longest side (H). In general, SSA will specify a singular triangle when the angle is opposite the <em>longest</em> specified side, regardless of that angle's measure. However, when the angle is opposite the <em>shortest</em> specified side, the above-described ratio restriction holds. If the sine of the angle is <em>less than</em> the ratio of sides, then <em>two possible triangles are specified</em>.

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