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Oxana [17]
3 years ago
7

g A popular theory is that presidential candidates have an advantage if they are taller than their main opponents. Listed are he

ights​ (in centimeters) of randomly selected presidents along with the heights of their main opponents. Complete parts​ (a) and​ (b) below. Height (cm )of President 191 180 180 182 197 180 Height (cm )of Main Opponent 166 179 168 183 194 186 a. Use the sample data with a 0.05 significance level to test the claim that for the population of heights for presidents and their main​ opponents, the differences have a mean greater than 0 cm. In this​ example, mu Subscript d is the mean value of the differences d for the population of all pairs of​ data, where each individual difference d is defined as the​ president's height minus their main​ opponent's height. What are the null and alternative hypotheses for the hypothesis​ test?
Mathematics
1 answer:
stira [4]3 years ago
5 0

Answer:

Step-by-step explanation:

Corresponding heights of presidents and height of their main opponents form matched pairs.

The data for the test are the differences between the heights.

μd = the​ president's height minus their main​ opponent's height.

President's height. main opp diff

191. 166. 25

180. 179. 1

180. 168. 12

182. 183. - 1

197. 194. 3

180. 186. - 6

Sample mean, xd

= (25 + 1 + 12 - 1 + 3 + 6)/6 = 5.67

xd = 5.67

Standard deviation = √(summation(x - mean)²/n

n = 6

Summation(x - mean)² = (25 - 5.67)^2 + (1 - 5.67)^2 + (12 - 5.67)^2+ (- 1 - 5.67)^2 + (3 - 5.67)^2 + (- 6 - 5.67)^2 = 623.3334

Standard deviation = √(623.3334/6 sd = 10.19

For the null hypothesis

H0: μd ≥ 0

For the alternative hypothesis

H1: μd < 0

The distribution is a students t. Therefore, degree of freedom, df = n - 1 = 6 - 1 = 5

The formula for determining the test statistic is

t = (xd - μd)/(sd/√n)

t = (5.67 - 0)/(10.19/√6)

t = 1.36

We would determine the probability value by using the t test calculator.

p = 0.12

Since alpha, 0.05 < than the p value, 0.12, then we would fail to reject the null hypothesis.

Therefore, at 5% significance level, we can conclude that for the population of heights for presidents and their main​ opponents, the differences have a mean greater than 0 cm.

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Solve the system using substitution.
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Answer:

Given: The following system:

4x + y − 2z=18          ......[1]

2x-3y+3z = 21          ......[2]

x-3y=6                      ......[3]

we can write equation [3] as;

3y = x-6                     ......[4]

Multiply by 3 in equation [1] to both sides of an equation we get,

3 \cdot(4x+y-2z)= 3\cdot 18 or

12x+3y-6z=54              ......[5]

Substituting the equation [4] in [2] and [5] we get;

2x-(x-6)+3z=21 or

2x-x+6+3z=21

Simplify:

x+3z=15            .....[6]                       [combine like terms]

12x+x-6-6z =54

Simplify:

13x-6z=60         ......[7]        [Combine like terms]

On Solving equation [6] and [7] simultaneously,

x+3z=15

13x-6z=60

we get the value of x

i.e, x=6

Substitute the value of x in equation x+3z=15  we get

6+3z=15 or

3z=9

Simplify:

z=3

Also, substitute the value of x=6 in equation [3] we get the value of y;

x-3y=6

6-3y=6 or

-3y = 0

Simplify:

y = 0

Therefore, the solution to the system of three linear equation is, (6, 0 , 3)


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kicyunya [14]
He will put $122 dollars into each account.

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Which equation can be used to solve 3/5 divided by 7/10
Jlenok [28]

Answer:

35/50

Step-by-step explanation:

Here we will show you how to calculate 3/5 divided by 7/10. We will give you the answer in fraction form and in decimal form.

Here is 3/5 divided by 7/10 displayed

3/5 ÷ 7/10

The numbers in 3/5 divided by 7/10 are labeled below:

3 = dividend numerator

5 = dividend denominator

7 = divisor numerator

10 = divisor denominator

To make it a fraction form answer, you multiply the dividend numerator by the divisor denominator to make a new numerator.

Furthermore, you multiply the dividend denominator by the divisor numerator to make a new denominator:

3 x 10/5 x 7 = 30/35

Thus, the answer to 3/5 divided by 7/10 in fraction form is:

30/50

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Here, we have,
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Using Formula,
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