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viva [34]
3 years ago
12

A researcher conducts a hypothesis test using a sample of n = 40 from an unknown population. What is the df value for the t stat

istic?
a. 38
b. 39
c. 40
d. 41
Mathematics
1 answer:
aliya0001 [1]3 years ago
3 0

Answer:

Correct option: b 39.

Step-by-step explanation:

A one-sample (or one mean) t-test is applied to test whether the population-parameter is significantly different from some hypothetical value.

The degrees of freedom of the <em>t</em>-test is:

df = n - 1

It is provided that the sample size is, <em>n</em> = 40.

Compute the degrees of freedom as follows:

df = n - 1

   = 40 - 1

   = 39

Thus, the correct option is b.

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Solve the triangle given that a=19 b=16, c=11.
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Answer:

The angles of the triangle are approximately 87.395º, 57.271º and 35.334º.

Step-by-step explanation:

From statement we know all sides of the triangle (a, b, c), but all angles are unknown (A, B, C). (Please notice that angles with upper case letters represent the angle opposite to the side with the same letter but in lower case) From Geometry it is given that sum of internal angles of triangles equal 180º, we can obtain the missing information by using Law of Cosine twice and this property mentioned above.

If we know that a = 19, b = 16 and c = 11, then the missing angles are, respectively:

Angle A

a^{2} = b^{2}+c^{2}-2\cdot b\cdot c \cdot \cos A (1)

A = \cos^{-1}\left(\frac{b^{2}+c^{2}-a^{2}}{2\cdot b\cdot c} \right)

A = \cos^{-1}\left[\frac{16^{2}+11^{2}-19^{2}}{2\cdot (16)\cdot (11)} \right]

A \approx 87.395^{\circ}

Angle B

b^{2} = a^{2}+c^{2}-2\cdot a\cdot c \cdot \cos B (2)

B = \cos^{-1}\left(\frac{a^{2}+c^{2}-b^{2}}{2\cdot a\cdot c} \right)

B = \cos^{-1}\left[\frac{19^{2}+11^{2}-16^{2}}{2\cdot (19)\cdot (11)} \right]

B\approx 57.271^{\circ}

Angle C

C = 180^{\circ}-A-B

C = 180^{\circ}-87.395^{\circ}-57.271^{\circ}

C = 35.334^{\circ}

The angles of the triangle are approximately 87.395º, 57.271º and 35.334º.

8 0
3 years ago
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