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
pantera1 [17]
3 years ago
12

The local branch of the Internal Revenue Service spent an average of 21 minutes helping each of 10 people prepare their tax retu

rns. The standard deviation was 5.6 minutes. A volunteer tax preparer spent an average of 27 minutes helping 14 people prepare their taxes. The standard deviation was 4.3 minutes. At α = 0.02, is there a difference in the average time spent by the two services? Find the 98% confidence interval for the two means.
a. State the hypotheses and identify the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
Mathematics
1 answer:
AURORKA [14]3 years ago
5 0

Answer:

The confidence Interval is [- 0.7053  10.4521]

a: The  hypotheses  are

H0: μ1=μ2    against the claim Ha :μ1≠μ2

b. The critical value for t∝/2 for 17 d.f  t > 2.508 and  t < -2.111

c. t= -2.8422

d. The calculated value of t= -2.8422 is less than t < -2.11 the critical value therefore we reject H0 and conclude there is a difference between the two means.

Step-by-step explanation:

When the standard deviations are not the same then the confidence intervals for mean differences are calculated as

(x1`-x2`)- t∝/2 √s1²/n1 + s2²/n2 < u1-u2 < (x1`-x2`)+ t∝/2 √s1²/n1 + s2²/n2

x1`= 21        x2`= 27

n1=  10       n2= 14

s1= 5.6       s2= 4.3

The degrees of freedom is calculated using

υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1

= 17

The t∝/2 for 17 d.f = 2.11

Putting the values

(x1`-x2`)- t∝/2 √s1²/n1 + s2²/n2 < u1-u2 < (x1`-x2`)+ t∝/2 √s1²/n1 + s2²/n2

(21-27) - 2.11√5.6²/10+ 4.3²/14 < u1-u2 <(21-27)  +2.11√5.6²/10+4.3²/14

6- 2.11*2.111 < u1-u2 <  ( 6 )  +2.11*2.111

6- 4.4521 < u1-u2 <  ( 6 )  +5.294

- 1.5479 < u1-u2 <  10.4521

The confidence Interval is [- 0.7053  10.4521]

a: The  hypotheses  are

H0: μ1=μ2    against the claim Ha :μ1≠μ2

The claim is that there is a difference in the average time spent by the two services

b. The critical value for t∝/2 for 17 d.f  t > 2.508 and  t < -2.111

The degrees of freedom is calculated using

υ = [s₁²/n1 + s₂²/n2]²/ (s₁²/n1 )²/ n1-1 + (s₂²/n2)²/n2-1

= 17

c. The test statistic is

t= (x1`-x2`)  /√s1²/n1 + s2²/n2

t= (21-27)  /√5.6²/10+ 4.3²/14

t= -6/2.111

t= -2.8422

d. The calculated value of t= -2.8422 is less than t < -2.11 the critical value therefore we reject H0 and conclude there is a difference between the two means.

You might be interested in
Find the length of side x in simplest radical form with a rational denominator.60°130°X
iren [92.7K]

We will solve using the law of sines as follows:

\frac{1}{\sin(30)}=\frac{X}{\sin (60)}

Now, we solve for X:

\Rightarrow X=\frac{\sin(60)}{\sin(30)}\Rightarrow X=\sqrt[]{3}

So, the length of X is sqrt(3).

5 0
1 year ago
Plot the following ordered pairs on a graph and then determine whether or not the points represent a function.
Alex777 [14]
The answer is :

YES: These points represent a function because none of the vertical lines I drew passed through more than one point.
5 0
3 years ago
Read 2 more answers
Because a square is a rectangle,it must have
yaroslaw [1]

Answer:

4 right angles & 2 sets of parallel lines

Step-by-step explanation:

i am big brain

5 0
3 years ago
The average value of a function f over the interval [−2,3] is −6 , and the average value of f over the interval [3,5] is 20. Wha
Xelga [282]

Answer:

The average value of f over the interval [-2,5] is \frac{10}{7}.

Step-by-step explanation:

Let suppose that function f is continuous and integrable in the given intervals, by integral definition of average we have that:

\frac{1}{3-(-2)} \int\limits^{3}_{-2} {f(x)} \, dx = -6 (1)

\frac{1}{5-3} \int\limits^{5}_{3} {f(x)} \, dx = 20 (2)

By Fundamental Theorems of Calculus we expand both expressions:

\frac{F(3)-F(-2)}{3-(-2)} = -6

F(3) - F(-2) = -30 (1b)

\frac{F(5)-F(3)}{5-3} = 20

F(5) - F(3) = 40 (2b)

We obtain the average value of f over the interval [-2, 5] by algebraic handling:

F(5) - F(3) +[F(3)-F(-2)] = 40 + (-30)

F(5) - F(-2) = 10

\frac{F(5)-F(-2)}{5-(-2)} = \frac{10}{5-(-2)}

\bar f = \frac{10}{7}

The average value of f over the interval [-2,5] is \frac{10}{7}.

4 0
3 years ago
Y = x +4<br> 3x + y = 16
Vesna [10]

Answer:

x= 3 while fo y = 7 that's the answer

5 0
3 years ago
Other questions:
  • Is This graph possible 60 POINTS
    11·2 answers
  • Given: line DR tangent to Circle O.<br><br> If m angle C = 63°, then m angle BDR =
    7·2 answers
  • If a 100-pound block of ice is placed on an inclined plane that makes an angle of 35° with the horizontal, how much friction for
    5·1 answer
  • Mary made 5 different sandwiches: turkey, roast beef, ham, bologna, and salami Mary wrapped the sandwiches and placed them into
    12·1 answer
  • The square of a whole number is between 1500 and 1600. The number must be between
    8·2 answers
  • What is the y-intercept of a line that has a slope of –3 and passes through point (–5, 4)? –17 , –11 , 7 , 19
    10·2 answers
  • A triangle has an area of 30 cm². The base and height are scaled by a factor of 3.
    13·1 answer
  • PLEASE HELP i don’t understand
    5·1 answer
  • What's the selling price if the markup is 45% and the cost to store 130
    10·1 answer
  • Ok i need helpppp...............
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!