A researcher wants to compare the heights of males between generations to see if they differ. To do this, he samples random pairs of males who are at least 18 years old and their fathers. He then splits them into a sample of fathers and a sample of sons. Suppose that data were collected for a random sample of 11 pairs, where each difference is calculated by subtracting the height of the son from the height of the father. Assume that the heights are normally distributed. The test statistic is t≈1.971, α=0.05, the corresponding rejection regions are t<−2.228 and t>2.228, the null hypothesis is H0:μd=0, and the alternative hypothesis is Ha:μd≠0.

Select all that apply:
a. Reject the null hypothesis.
b. Fail to reject the null hypothesis.
c. The conclusion of the hypothesis test is that there is sufficient evidence to suggest that the heights of males between generations are different.
d. The conclusion of the hypothesis test is that there is insufficient evidence to suggest that the heights of males between generations are different.

Answers

Answer 1

Answer:

The correct option is  

Option A and Option C

Step-by-step explanation:

From the question we are told that

   The sample size of paired men is  [tex]n_p   =  11[/tex]

   The test statistics is  t≈1.971

    The  significance level is  α=0.05

    The rejection region is  t<−2.228 and t>2.228

    The null hypothesis is  [tex]H_o :\mu_ d=0[/tex]

     The alternative hypothesis  is  [tex]H_a :\mu_ d \ne 0[/tex]

Generally the degree of freedom is mathematically represented as

        [tex]df  =  n_1 +  n_2 - 2[/tex]

Here [tex]n_1[/tex] is the sample size of  father which is  [tex]n_1 =  11[/tex]

        [tex]n_2[/tex] is the sample size of males who are at least 18 years old  which is  [tex]n_2 =  11[/tex]

So

     [tex]df  =  11 +  11 - 2[/tex]

=>   [tex]df  =  20[/tex]

Generally the critical values of  α=0.05 from the  t- distribution table at a degree of freedom of  [tex]df  =  20[/tex]  for a two -tailed test  is  

     [tex]t_{0.05 , 20 } =  \pm 2.08596345  [/tex]

From the value  obtained we see that the critical value  is within the region of rejection hence

 The decision rule is

Reject the null hypothesis

The conclusion is  

  The conclusion of the hypothesis test is that there is sufficient evidence to suggest that the heights of males between generations are different.

     


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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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I think it’s the third one. As the radius increases, so does the area.

Is the square root of 14 +6.2 less than 3 pi - 8.2?

Answers

Answer:

No. √14 + 6.2 is more than 3π - 8.2

Step-by-step explanation:

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If a histogram of a sample of​ men's ages is​ skewed, what do you expect to see in the normal quantile​ plot?

Answers

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Step-by-step explanation:

Histograms are used to show the distribution of a dataset.

If the histogram is skewed, then it means that the points do not follow a straight-line pattern, on the normal quantile plot.

From the question, we understand that:

The histogram is skewed

This means that:

The data points of the histogram are either concentrated on the right or on the left-hand side of the histogram.

The above highlight mean that:

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Answers

Answer:

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Step-by-step explanation:

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Answers

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A TV show has 26 episodes. Due to the lack of time, you can onlywatch 5 of them. However, in order to get a gist of what the showis about, you do not want to watch any two consecutive episodes.How many selections of 5 episodes are there with no two consecutiveepisodes chosen? Assuming that the order of selection is irrelevant.(Hint:this is a Stars and Bars problem)

Answers

Answer:

Step-by-step explanation:

Recall that: The number of combination to select any k consecutive element from n consecutive term is given by the equation [tex]^{n-k+1}C_k[/tex]

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[tex]^{n-k+1}C_k= \begin {pmatrix} ^{26-5+1}_{5} \end {pmatrix}[/tex]

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Answers

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Given that, 24 divided by 4 is 6.

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So, the remainder is 0.

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Answers

Answer:

Step-by-step explanation:

[tex]\frac{f(b)-f(a)}{b-a}[/tex] This is the formula for the average rate of change

over the interval (a, b)

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

x = 150

Step-by-step explanation:

We know a circle is 360°, so the angles must add up to 60°.

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Answers

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

Answer:

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9514 1404 393

Answer:

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Answers

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[tex]\huge\boxed{a=4}[/tex]

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A spherical balloon is inflated with gas at a rate of 500 cubic centimeters per minute. Find the rates of change of the radius when r = 70 centimeters and r = 95 centimeters.

Answers

Answer:

for r= 70 cm

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Step-by-step explanation:

kindly find attached a rough sketch of the circle and a detailed solution of the problem.

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Answers

Answer:

= 3/4

Step-by-step explanation:

Find 2 points on the graph

(2,3) and (6,6)

Using the slope formula

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   = ( 6-3)/(6-2)

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Rachel is recording the temperature at her school every morning this week. On Monday, the temperature was 5°C. Part A: On Wednesday, Rachel calculated that the temperature was 13 degrees colder than Monday. What temperature did Rachel record on Wednesday? Part B: On Friday, Rachel calculated that the temperature was 4 degrees warmer than Wednesday. What temperature did Rachel record on Friday?​

Answers

Answer:

Part A: -8

Part B: -4

Step-by-step explanation:

[tex]5-13=-8[/tex]

[tex]-8+4=-4[/tex]

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Let c represent the weight of each box Caleb lifted.

Which expression represents the total number of pounds Sergio lifted?


120c

10(c−12)

12(c+10)

c + 10

Answers

Answer:

b

Step-by-step explanation:

Answer:

12 c+10

Step-by-step explanation:

becus

13
In the figure shown below, if line mis parallel to line n, then find the value of x. (This is a 2 part question.)
m
(2x-10)
(65 - x)
Part A
Write the equation to find the value of x. (DO NOT find x, just write the equation.)
(2x - 10) (65 - x)
Part B
What is the value of x?
Y

Answers

Answer:

2x-10 = 65-x

Step-by-step explanation:

just add up both alternate internal angles as they are both equal

so, the equation is: 2x-10 = 65-x

Answer:

The right equation will be 2x - 10 = 65 - x (you were wrong lol)

Step-by-step explanation:

We have: 2x - 10 = 65 - x

=> 2x - 10 + x = 65

=> 3x = 65 + 10 = 75

=> x = 75/3 = 25

P/S: After some little chats with the others, this might be wrong :(

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