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
DiKsa [7]
3 years ago
12

A Survey of 85 company employees shows that the mean length of the Christmas vacation was 4.5 days, with a standard deviation of

1.2 days. Construct a 95% confidence interval for the population's mean length of vacation. ( , ) Round your answer to two decimal digits Construct a 92% confidence interval for the population's mean length of vacation. ( , ) Round your answer to two decimal digits
Mathematics
1 answer:
GenaCL600 [577]3 years ago
8 0

Answer:

The 95% confidence interval for the population's mean length of vacation, in days, is (4.24, 4.76).

The 92% confidence interval for the population's mean length of vacation, in days, is (4.27, 4.73).

Step-by-step explanation:

We have the standard deviations for the sample, which means that the t-distribution is used to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 85 - 1 = 84

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 84 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.95}{2} = 0.975. So we have T = 1.989.

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 1.989\frac{1.2}{\sqrt{85}} = 0.26

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 4.5 - 0.26 = 4.24 days

The upper end of the interval is the sample mean added to M. So it is 4.5 + 0.26 = 4.76 days

The 95% confidence interval for the population's mean length of vacation, in days, is (4.24, 4.76).

92% confidence interval:

Following the sample logic, the critical value is 1.772. So

M = T\frac{s}{\sqrt{n}} = 1.772\frac{1.2}{\sqrt{85}} = 0.23

The lower end of the interval is the sample mean subtracted by M. So it is 4.5 - 0.23 = 4.27 days

The upper end of the interval is the sample mean added to M. So it is 4.5 + 0.23 = 4.73 days

The 92% confidence interval for the population's mean length of vacation, in days, is (4.27, 4.73).

You might be interested in
White has of the following is true a. The angle of elevation
Solnce55 [7]
The answer is b I believe
7 0
3 years ago
Read 2 more answers
Are the graphs of y= 1/3x-4 and y-2=-3(x-4) parallel, perpendicular, or neither
melamori03 [73]

Answer:

ghtrh

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
Kenneth loaned $1,200 to his niece to buy a computer. Two years later, she paid him back the $1,200 along with an interest of $9
insens350 [35]

Answer:

<u>The  annual interest rate was 4%</u>

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Loan to Kenneth's niece to buy a computer = US$ 1,200

Duration of the loan = 2 years

Niece paid back to Kenneth = US$ 1,296

Annual interest rate = x%

2. Let's find the annual interest rate after 2 years, using the following formula:

FV = PV * (1 + x)

PV = Loan to Kenneth's niece to buy a computer = US$ 1,200

FV = Niece paid back to Kenneth = US$ 1,296

rate (r) = x

Replacing with the real values:

1,296 = 1,200 * (1 + x)

1.296/1.200 = (1 + x) (Dividing by 1,200 at both sides)

1.08 = 1 + x

1.08 - 1 = x (Subtracting 1 at both sides)

<u>0.08 = x</u>

This is the interest rate for two years, for finding the annual interest rate we divide it by 2, this way:

<u>0.08 / 2 = 0.04 * 100 = 4%</u>

7 0
3 years ago
10. The numbers —12, —7, —2, 3... follow a pattern. What are the next three numbers in this pattern? 7, 11, 16 5, 10, 15 2, 7, 1
Alik [6]
The answer is 8, 13, 18
4 0
3 years ago
A spinner is divided into 13 equal-sized sections, and each section is labeled with a number 1 through 13.
nikitadnepr [17]

Answer:

10/13

Step-by-step explanation:

if this is wrong, im sorry, but im pretty sure its correct

5 0
3 years ago
Other questions:
  • In a billiards game, Pete hits a ball that is 20in. from a wall. The ball travels 34 in. until it hits the wall and bounces to a
    10·1 answer
  • What is not preserved under dilation? Select all that apply.
    8·1 answer
  • Suppose you have 40 meters of fencing what is the greatest rectangular area that you can enclose
    15·1 answer
  • PLEASE HELP!! 35POINTS!!
    15·1 answer
  • a battery company manufactures batteries having life spans that are normally distributed, with a mean of 45 months and a standar
    9·2 answers
  • 10 points plz help me
    14·1 answer
  • Simplify the expression (3+i)(2+i)
    10·2 answers
  • What the answer for 8x+1+7x+4
    11·1 answer
  • You're given two side lengths of 10 centimeters and 8 centimeters. The angle between the sides measures 40°. How many triangles
    10·1 answer
  • Will give Brainly if correct
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!