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
anastassius [24]
3 years ago
7

A researcher is concerned about the impact of students working while they are enrolled in classes, and she likes to know if stud

ents work too much and therefore are spending less time on their classes than they should be. The researcher chooses a sample of 150 students and found that the sample mean is 7.10 hours and the sample standard deviation is 5. Construct a 90% confidence interval estimate of the mean hours a week students are working. a. What is the point estimate: _____________b. Find the critical value: ________________ Round to 3 decimal places. c. What is the margin or error: __________________ Round the answer to three decimal places d. Construct the confidence interval: Express the answer as (x,x), ______________ round to one decimal place. e. State the final Conclusion.
Mathematics
1 answer:
8_murik_8 [283]3 years ago
6 0

Answer:

(a) Point estimate = 7.10

(b) The critical value is 1.960

(c) Margin of error = 0.800

(d) Confidence Interval = (6.3, 7.9)

(e) We are 90% confident that the average number of hours worked by the students is between 6.3 and 7.9

Step-by-step explanation:

Given

\bar x = 7.10 -- sample mean

\sigma=5 --- sample standard deviation

n = 150 --- samples

Solving (a): The point estimate

The sample mean can be used as the point estimate.

Hence, the point estimate is 7.10

Solving (b): The critical value

We have:

CI = 90\% --- the confidence interval

Calculate the \alpha level

\alpha = 1 - CI

\alpha = 1 - 90\%

\alpha = 1 - 0.90

\alpha = 0.10

Divide by 2

\frac{\alpha}{2} = 0.10/2

\frac{\alpha}{2} = 0.05

Subtract from 1

1 - \frac{\alpha}{2} = 1 - 0.05

1 - \frac{\alpha}{2} = 0.95

From the z table. the critical value for 1 - \frac{\alpha}{2} = 0.95 is:

z = 1.960

Solving (c): Margin of error

This is calculated as:

E = z * \frac{\sigma}{\sqrt n}

E = 1.960 * \frac{5}{\sqrt {150}}

E = 1.960 * \frac{5}{12.25}

E =  \frac{1.960 *5}{12.25}

E =  \frac{9.80}{12.25}

E =  0.800

Solving (d): The confidence interval

This is calculated as:

CI = (\bar x - E, \bar x + E)

CI = (7.10 - 0.800, 7.10 + 0.800)

CI = (6.3, 7.9)

Solving (d): The conclusion

We are 90% confident that the average number of hours worked by the students is between 6.3 and 7.9

You might be interested in
Write the equation of a horizontal line that passes through the point (3,-3).
cestrela7 [59]
Hello : 
 the equation is : y -(-3) = 0(x-3)....(slope = 0 '<span>horizontal line')
y=-3</span>
4 0
3 years ago
Convert 27day 8hour into second
Nataliya [291]
27 days and 8 hours = 656 hours
27 x 24 = 648
648 + 8 = 656
24 hours = 3,600 seconds
656 x 3,600 = 2,361,600 seconds

The answer is 2,361,600 seconds.
7 0
3 years ago
Your work or words should justify your answer (explain how you know). As a math teacher, Josie frequently makes photocopies of f
Doss [256]

Answer:

Yes, because by dividing x by his equivalent y, you find a constant of proportionality being 10.

x / y = 10

Step-by-step explanation:

20 / 2 = 10

50 / 5 =10

60 / 6 = 10

70 / 7 = 10

7 0
3 years ago
Use the identity (x+y)(x^2−xy+y^2)=x^3+y^3 to find the sum of two numbers if the product of the numbers is 28, the sum of the sq
lara31 [8.8K]

Step-by-step explanation:

We have xy = 28, x² + y² = 65 and x³ + y³ = 407.

Since (x + y)(x² - xy + y²) = x³ + y³,

x + y = (x³ + y³)/(x² + y² - xy)

= (407) / [(65) - (28)]

= 407 / 37

= 11.

Hence the sum of the numbers is 11.

4 0
3 years ago
Read 2 more answers
Write 80 as the product of its prime factors
ehidna [41]

Answer:

2 * 2 * 2 * 2 * 5.

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • Twelve people are standing in line to buy movie tickets. The theater is running a promotion by giving away 2 concession stand gi
    9·1 answer
  • What are prime numbers
    15·2 answers
  • Express - 64 by 112 as a rational number with denominator 7​ .plz answer fast so l will follow you .
    9·2 answers
  • Find the least common multiple of each set of numbers 9,12,15
    15·1 answer
  • What is the value of a + bc when a=7, b = 4 and c = 1/2
    5·1 answer
  • What is an equation of the line that passes through the points (-2,8) and (1, -1)? ​
    10·1 answer
  • What is -6x multiplied by y
    6·2 answers
  • please find the area
    6·1 answer
  • Ivana has two identical dice and on the faces of each are the numbers −3, −2, −1, 0, 1, 2.
    7·1 answer
  • If six cans of soda cost nine dollars, how much would it cost for 8 cans.
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!