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
grandymaker [24]
2 years ago
7

A study was conducted to estimate the difference in the mean salaries of elementary school teachers from two neighboring states.

A sample of 10 teachers from the Indiana had a mean salary of $28,900 with a standard deviation of $2300. A sample of 14 teachers from Michigan had a mean salary of $30,300 with a standard deviation of $2100. Determine a 95% confidence interval for the difference between the mean salary in Indiana and Michigan.(Assume population variances are different.)
Mathematics
1 answer:
umka21 [38]2 years ago
6 0

Answer:

(28900-30300) -2.07 \sqrt{\frac{2300^2}{10} +\frac{2100^2}{14}} = -3301.70

(28900-30300) +2.07 \sqrt{\frac{2300^2}{10} +\frac{2100^2}{14}} = 501.698

The confidence interval would be -3301.70 \leq \mu \leq 501.698 and since the confidence interval contains the value of 0 we don't have enough evidence to conclude that the difference between the two states for the salary of teachers are significantly different.

Step-by-step explanation:

We have the following info given by the problem

\bar X_1 = 28900 the sample mean for the salaries of teachers in Indiana

s_1 = 2300 the sample deviation for the salary of  teachers in Indiana

n_1 =10 the sample size from Indiana

\bar X_2 = 30300 the sample mean for the salaries of teachers in Michigan

s_2 = 2100 the sample deviation for the salary of  teachers in Michigan

n_2 =14 the sample size from Michigan

We want to find a confidence interval for the difference in the two means and the formula for this case is given by;

(\bar X_1 -\bar X_2) \pm t_{\alpha/2}\sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}

The degrees of freedom for this case are:

df = n_1 +n_2 -2= 10+14-2 =22

The confidence is 95%so then the significance is \alpha=0.05 and the \alpha/2 =0.025, we need to find a critical value in the t distribution with 22 degrees of freedom who accumulates 0.025 of the area on each tail and we got:

t_{\alpha/2}= 2.07

And now replacing in the formula for the confidence interval we got:

(28900-30300) -2.07 \sqrt{\frac{2300^2}{10} +\frac{2100^2}{14}} = -3301.70

(28900-30300) +2.07 \sqrt{\frac{2300^2}{10} +\frac{2100^2}{14}} = 501.698

The confidence interval would be -3301.70 \leq \mu \leq 501.698 and since the confidence interval contains the value of 0 we don't have enough evidence to conclude that the difference between the two states for the salary of teachers are significantly different.

You might be interested in
How would i figure this out
arsen [322]

9514 1404 393

Answer:

  see attached

Step-by-step explanation:

To plot the line through the point, plot the point. Then find another point that has the given "rise" and "run". Draw the line through the two points.

__

The given point is (-7, -4). Locate that on the graph.

The slope is given as -2/3. This is the ratio of "rise" to "run", so it means the "rise" will be -2 for each "run" of 3. (rise/run = -2/3)

The rise is the vertical change. So, you want your second point to be 2 units below the given point. Its y-coordinate will be -4-2 = -6.

The run is the horizontal change. Your second point will be 3 units to the right of the given point, so its x-coordinate will be -7+3 = -4. Now, you can plot the point (-4, -6) and draw your graph through these two points.

4 0
3 years ago
the model shows -3x + 5= -2x -1. What value of x makes the equation true? look at the picture please..
Stels [109]

Answer:

D. x=6

Step-by-step explanation:

-3x + 5= -2x -1

more variables to left hand side and change its sign

-3x+2x+5=-1

move constant to right hand side and change its sign

-3x+2x=-1-5

collect like terms

-x=-1-5

calculate the difference

-x=-6

change the signs on both sides of the equation

x=6

5 0
3 years ago
Simply 3 small 2+8x4 need answer
evablogger [386]

Answer:

2+32

34

Step-by-step explanation:

First we should multiply before adding after multiplying 8×4 is 32 and add 32+2 then it is 34

7 0
3 years ago
Read 2 more answers
Max buys fabric that is 9 1/2 feet long. The cost of the fabric is $0.70 per foot, including tax. What is the total cost, in dol
Tanya [424]
Total cost= 9.5(.70) =6.65
5 0
3 years ago
What is the solution to the equation 9r=4/7
Vera_Pavlovna [14]

Answer:

r=4/63

Step-by-step explanation:

Divide each term in 9r=47 by 9 and simplify.

8 0
2 years ago
Read 2 more answers
Other questions:
  • Jack works for a company that pays him $20 an hour. His normal workday does not exceed 8 hours. After working 8 hours in a day,
    13·1 answer
  • Please help me with this question, image attached.
    11·2 answers
  • A rancher has 200 ft of fencing to enclose two adjacent rectangular corrals.
    13·1 answer
  • The output value of a function is represented by P(200). What is the input value for this function?
    6·1 answer
  • Evaluate 7c4<br> a. 6<br> b. 1<br> c. 35<br> d. 840
    13·2 answers
  • Please help solve!!! Thank you!!
    7·1 answer
  • Kat is painting the edge of a triangular stage prop with reflective orange paint. The lengths of the edges of the triangle are (
    12·2 answers
  • If 24 apples represents 30% of her apple supply. How many total apples does Jasmine have?
    11·2 answers
  • Find the vector that translate A (-2, 7) to A' (6,4) *
    10·2 answers
  • What is the volume of the figure?<br> 11m 7m and. 4m
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!