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Anna35 [415]
3 years ago
15

To test the belief that sons are taller than their​ fathers, a student randomly selects 13 fathers who have adult male children.

She records the height of both the father and son in inches and obtains the following data. Are sons taller than their​ fathers? Use the alphaequals0.10 level of significance.​ Note: A normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers.
Height of Father Height of Son
72.4 77.5
70.6 74.1
73.1 75.6
69.9 71.7
69.4 70.5
69.4 69.9
68.1 68.2
68.9 68.2
70.5 69.3
69.4 67.7
69.5 67
67.2 63.7
70.4 65.5
Which conditions must be met by the sample for this​ test? Select all that apply.
A. The sample size is no more than​ 5% of the population size.
B. The differences are normally distributed or the sample size is large.
C. The sample size must be large.
D. The sampling method results in a dependent sample.
E. The sampling method results in an independent sample.
Write the hypotheses for the test. Upper
H 0 ​:
H 1 ​:
Calculate the test statistic. t 0=? ​
(Round to two decimal places as​ needed.)
Calculate the​ P-value. ​P-value=?
​(Round to three decimal places as​ needed.) Should the null hypothesis be​ rejected?
▼ Do not reject or Reject Upper H 0 because the​ P-value is ▼ less than or greater than the level of significance. There ▼ is or is not sufficient evidence to conclude that sons ▼ are the same height or are shorter than or are taller than or are not the same height as their fathers at the 0.10 level of significance. Click to select your answer(s).
Mathematics
1 answer:
KATRIN_1 [288]3 years ago
8 0

Answer:

1) B. The differences are normally distributed or the sample size is large

C. The  sample size mus be large

E. The sampling method results in an independent sample

2) The null hypothesis H₀:  \bar x_1 =  \bar x_2

The alternative hypothesis Hₐ: \bar x_1 <  \bar x_2

Test statistic, t = -0.00693

p- value = 0.498

Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers  at 0.10 level of significance

Step-by-step explanation:

1) B. The differences are normally distributed or the sample size is large

C. The  sample size mus be large

E. The sampling method results in an independent sample

2) The null hypothesis H₀:  \bar x_1 =  \bar x_2

The alternative hypothesis Hₐ: \bar x_1 <  \bar x_2

The test statistic for t test is;

t=\dfrac{(\bar{x}_1-\bar{x}_2)}{\sqrt{\dfrac{s_{1}^{2} }{n_{1}}-\dfrac{s _{2}^{2}}{n_{2}}}}

The mean

Height of Father, h₁,  Height of Son h₂

72.4,      77.5

70.6,      74.1

73.1,       75.6

69.9,      71.7

69.4,      70.5

69.4,      69.9

68.1,       68.2

68.9,      68.2

70.5,       69.3

69.4,       67.7

69.5,       67

67.2,       63.7

70.4,       65.5

\bar x_1  = 69.6      

s₁ = 1.58

\bar x_2 = 69.9

s₂ = 3.97

n₁ = 13

n₂ = 13

t=\dfrac{(69.908-69.915)}{\sqrt{\dfrac{3.97^{2}}{13}-\dfrac{1.58^{2} }{13}}}

(We reversed the values in the square root of the denominator therefore, the sign reversal)

t = -0.00693

p- value = 0.498 by graphing calculator function

P-value > α Therefore, we do not reject the null hypothesis

Do not reject Upper H₀ because, the P-value is greater than the level of significance. There is sufficient evidence to conclude that sons are the same height as their fathers  at 0.10 lvel of significance

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Anna007 [38]

Answer:

Part A: Angle R is not a right angle.

Part B; Angle GRT' is a right angle.

Step-by-step explanation:

Part A:

From the given figure it is noticed that the vertices of the triangle are G(-6,5), R(-3,1) and T(2,6).

Slope formula

m=\frac{y_2-y_1}{x_2-x_1}

The product of slopes of two perpendicular lines is -1.

Slope of GR is

\text{Slope of GR}=\frac{1-5}{-3-(-6)}=\frac{-4}{3}

Slope of RT is

\text{Slope of RT}=\frac{6-1}{2-(-3)}=\frac{5}{5}=1

Product of slopes of GR and RT is

\frac{-4}{3}\times 1=\frac{-4}{3}\neq -1

Therefore lines GR and RT are not perpendicular to each other and angle R is not a right angle.

Part B:

If vertex T translated by rule

(x,y)\rightarrow(x-1,y-2)

Then the coordinates of T' are

(2,6)\rightarrow(2-1,6-2)

(2,6)\rightarrow(1,4)

Slope of RT' is

\text{Slope of RT'}=\frac{4-1}{1-(-3)}=\frac{3}{4}

Product of slopes of GR and RT' is

\frac{-4}{3}\times \frac{3}{4}=-1

Since the product of slopes is -1, therefore the lines GR and RT' are perpendicular to each other and angle GRT' is a right angle.

6 0
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I got 67, is it right? Solve for angle A of the right triangle
Lina20 [59]
I think it would be 37 hope this helps:)

8 0
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A brother and a sister are in the same math class. there are 8 boys and 10 girls in the class. one boy and one girl are randomly
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5 0
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What is the volume of a cube with a higher base and width of 4cm
katrin2010 [14]
<h3>♫ - - - - - - - - - - - - - - - ~Hello There!~ - - - - - - - - - - - - - - - ♫</h3>

➷ Volume = height x base x width

Volume = 4 x 4 x 4

Volume = 64

The volume is 64cm^2

<h3><u>✽</u></h3>

➶ Hope This Helps You!

➶ Good Luck (:

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6 0
3 years ago
Square root of 648.7209 by division method
SpyIntel [72]

Answer:

25.47

Step-by-step explanation:

This root can be rewritten as:

\sqrt{\frac{6487209}{10000} }

\sqrt{\frac{6487209}{100^{2}} }

\frac{1}{100}\cdot \sqrt{6487209}

Since 6487209 is a multple of 3, the expression can be rearranged as follows:

\frac{1}{100}\cdot \sqrt{3\times 2162403}

2162403 is also a multiple of 3, then:

\frac{1}{100}\cdot \sqrt{3^{2}\times 720801}

\frac{3}{100}\cdot \sqrt{720801}

720801 is a multiple of 3, then:

\frac{3}{100}\cdot \sqrt{3\times 240267}

240267 is a multiple of 3, then:

\frac{3}{100}\times \sqrt{3^{2}\times 80089}

\frac{9}{100}\cdot \sqrt{80089}

80089 is a multiple of 283, then:

\frac{9}{100}\cdot \sqrt{283^{2}}

\frac{9\times 283}{100}

\frac{2547}{100}

25.47

6 0
3 years ago
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