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.

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.

Help me out please I need help

Harry has a part-time job as a babysitter. The table below shows the amount of money Harry earned for different numbers of hours of work:

Harry's Earnings from Babysitting
Number of Hours Worked Money Earned (dollars)
5 60
6 72
8
120

Part A: What are the missing numbers in the table? Show your work. (4 points)

Part B: Harry also does part-time yard work. The ratio of the number of hours Harry works in the yard to the money he earns in dollars is 1:10. Create a table to show the money earned by Harry for 5, 6, and 8 hours of work in the yard. (3 points)

Part C: How many more dollars does Harry earn working as a babysitter for 5 hours than doing yard work for 5 hours? Show your work. (3 points)

Explain how the sample proportion p-hat can be viewed as the sample mean X-bar.

Simplify the expression given below x-3/x-1 + 6/x-3 . A. B. C. D.

Solve 6x - 7y= 16 for y.

I need help with this question

Please help me with all the answers please say like 1: the answer 2: the answer like that thank you so much

6. Jack is x years old
Jill is 8 years older than Jack.
Mary is three times older than Mary.
The Sum of their ages is 67.
(a) Form a simplified equation in terms of x
(b) Solve the equation and work out Rebecca's Mary's and Jill's ages

Undefined slope, (0,-8)

find the distance between points P ( 7,8 ) and Q ( 6,2 )

If the area of the base of the box is 112 square inches and the height is 3.5 inches, what is the volume of the box?

Simplest form of 8/36

Find the difference. Express the answer in scientific notation.

(9.1 × 10–6) – (8.9 × 10–6)

2.0 × 10–7
0.2 × 10–6
2.0 × 10–6
2.0 × 10–5

14) What is 50% of 180?
15) What is 25% of 36?
16) What is 100% of 166?
17) What is 150% of 126?
18) What is 10% of 100?
19) What is 200% of 133?
20) What is 25% of 172?

BI
Challenge 2
A: Can you find the
area of the circle?
r=x +1
B: Can you find the
circumference of
the circle?

5 3/4 x 2 1/3 =? wut da answer?

Olga has $40 in her wallet. She has one more $5 bill than $10 bills, and two more $1 bills than $5 bills. If Olga has only three types of bills, how many bills of each denomination does she have?

Find the value of X.

Solve the proportion. 3/4=m/6

AMY HAS TWO TOMATO PLANTS. ONE IS 5 3/4 INCHES TALL AND THE OTHER IS 8 1/2 INCHES TALL. WHAT IS THE DIFFERENCE IN HEIGHT BETWEEN THE TWO TOMATO PLANTS?

express the following into standard form
[tex] \frac{1}{3500000000} [/tex]
​

Julie can type 250 words in 5 minutes. How long does she take to type 900 words!

Aaron can buy 4 tickets for $33. How much will it cost for 11 tickets?​

is 60 : 45 and 4 : 3 equlvalent ratios?

when writing fraction from a graph does the x axis number go on top or bottom​

|3x-4| less than or equal to 5

Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
a) Simplify the expression and explain each step. (2 points)
4(3x+2)−2
b) Factor the expression completely. (1 point)
20b−16

A scuba diver is 12 meters below sea level. If the diver descends 39 meters further, what integer represents the scuba diver’s new elevation relative to sea level?

To download movies off the internet, you must pay $1.99 per movie, plus a onetime fee of $5.50. Write an expression to show the total cost to download n movies.

Can someone help ME PLEASE?!!! will mark brainliest, a friend request, and will rate ur answer
Can someone write these down on a piece of paper?
THX A LOT FOR WHO EVER HELPS ME!!! :)