1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
julsineya [31]
3 years ago
13

A survey was conducted to determine the average age at which college seniors hope to retire in a simple random sample of 101 sen

iors, 55 was the
average desired retirement age, with a standard deviation of 3.4 years. A 96% confidence interval for desired retirement age of all college students is:
54.30 to 55.70
54.55 to 55.45
54.58 to 55.42
54 60 to 55.40
Mathematics
1 answer:
tatyana61 [14]3 years ago
7 0

Answer:

96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].

Step-by-step explanation:

We are given that a survey was conducted to determine the average age at which college seniors hope to retire in a simple random sample of 101 seniors, 55 was the  average desired retirement age, with a standard deviation of 3.4 years.

Firstly, the Pivotal quantity for 96% confidence interval for the population mean is given by;

                         P.Q. =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample average desired retirement age = 55 years

            \sigma = sample standard deviation = 3.4 years

            n = sample of seniors = 101

            \mu = true mean retirement age of all college students

<em>Here for constructing 96% confidence interval we have used One-sample t test statistics as we don't know about population standard deviation.</em>

<u>So, 96% confidence interval for the population mean, </u>\mu<u> is ;</u>

P(-2.114 < t_1_0_0 < 2.114) = 0.96  {As the critical value of t at 100 degree

                                               of freedom are -2.114 & 2.114 with P = 2%}  

P(-2.114 < \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } } < 2.114) = 0.96

P( -2.114 \times {\frac{s}{\sqrt{n} } } < {\bar X-\mu} < 2.114 \times {\frac{s}{\sqrt{n} } } ) = 0.96

P( \bar X-2.114 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X+2.114 \times {\frac{s}{\sqrt{n} } } ) = 0.96

<u>96% confidence interval for</u> \mu = [ \bar X-2.114 \times {\frac{s}{\sqrt{n} } } , \bar X+2.114 \times {\frac{s}{\sqrt{n} } } ]

                                           = [ 55-2.114 \times {\frac{3.4}{\sqrt{101} } } , 55+2.114 \times {\frac{3.4}{\sqrt{101} } } ]

                                           = [54.30 , 55.70]

Therefore, 96% confidence interval for desired retirement age of all college students is [54.30 , 55.70].

You might be interested in
Type your number answer in decimal form. Do not round. 3,000 millimeters =
nadezda [96]
3,000 millimeters = 3 meters. 

So, the answer should be 3.

Hope this helps :)


7 0
3 years ago
Read 2 more answers
What is the maximum value?
Pavel [41]

Answer:

the maximum value is 3

Step-by-step explanation:

The maximum value of the function y = -2+5sin(pi/12(x-2)) is determined by taking the first derivative of the function. The first derivative is equal ( 5 pi/ 12 )* sin ((pi/12) (x-2)) = 0. x is equal to 4472 through the calculator. Substituting to the original equation, the maximum value is 3.

5 0
3 years ago
Which of the following expressions represents the area of a trapezoid with bases of 3x and 5x and a height of 6x?
BaLLatris [955]
Trapezoid Area = (Base1 + Base2) (h/2)
so A = (3x + 5x )(6x/2)= 24x^2
6 0
3 years ago
so ive been haveing trouble in math and I need help.it would be nice if you solved the whole question
agasfer [191]

\frac{29}{3}
3 0
3 years ago
28 and 12<br> The GCF is
jok3333 [9.3K]

Answer: Greatest common factor (GCF) of 12 and 28 is 4. We will now calculate the prime factors of 12 and 28 then find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 12 and 28.

Step-by-step explanation: BRAINLESS PLEASE

8 0
3 years ago
Other questions:
  • HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
    11·1 answer
  • A leaf hangs from a branch 12 feet in the air. It falls to the ground at a rate of 0.25 feet per second. Which graph could repre
    13·2 answers
  • The physics department of a college has 8 male professors, 11 female professors, 16 male teaching assistants, and 6 female teach
    15·2 answers
  • How do you simplify 29/40
    13·2 answers
  • How many times can 475 go into 1,662?
    9·2 answers
  • √70 is between which two numbers on the number line?
    14·1 answer
  • 2x 1/2 x3 2/3 im goin to be need a lot of helpppp
    13·2 answers
  • Please help! i’ve been stuck on this for over 10 minutes.
    11·1 answer
  • Need help with page 16 and 19
    15·1 answer
  • PPPLLLEEEAAASSSE HHHEEELLLPPP! 14 points! Brainlliest, hearts, and stars!
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!