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
Vlada [557]
3 years ago
8

Money Spent on Road Repair A politician wishes to compare the variances of the amount of money spent for road repair in two diff

erent counties. The data are given here. At α = 0.05, is there a significant difference in the variances of the amounts spent in the two counties? Use the P-value method.
County A County B
s1 = $11,596 s2 = $14,837
n1 = 15 n2 = 18
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:
Mkey [24]3 years ago
7 0

Answer:

(A) Null Hypothesis, H_0 : \sigma_1^{2} =\sigma_2^{2}      {means that there is no significant difference in the variances of the amounts spent in the two counties}

Alternate Hypothesis, H_A : \sigma_1^{2} \neq \sigma_2^{2}      {means that there is a significant difference in the variances of the amounts spent in the two counties}

(B) The F-table gives critical values of 0.359 and 2.781 for (14,17) degrees of freedom for the two-tailed test.

(C) The value of the F-test statistic is 0.611.

(D) We conclude that there is no significant difference in the variances of the amounts spent in the two counties.

Step-by-step explanation:

We are given that a politician wishes to compare the variances of the amount of money spent on road repair in two different counties.

The data are given here below;

County A              County B

s1 = $11,596         s2 = $14,837

n1 = 15                     n2 = 18

Let \sigma_1^{2} = variances of the amounts spent in County A.

\sigma_2^{2} = variances of the amounts spent in County B.

(A) So, Null Hypothesis, H_0 : \sigma_1^{2} =\sigma_2^{2}      {means that there is no significant difference in the variances of the amounts spent in the two counties}

Alternate Hypothesis, H_A : \sigma_1^{2} \neq \sigma_2^{2}      {means that there is a significant difference in the variances of the amounts spent in the two counties}

The test statistics that would be used here <u>Two-sample F-test statistics </u>distribution;

                             T.S. =  \frac{s_1^{2} }{s_2^{2} } \times \frac{\sigma_2^{2} }{\sigma_1^{2} }  ~ F__n_1_-_1,_ n_2_-_1

where, s_1 = sample standard deviation for County A = $11,596

s_2 = sample standard deviation for County B = $14,837

n_1 = sample size for County A = 15

n_2 =  sample size for County B = 18

(B) Now at 0.05 level of significance, the F-table gives critical values of 0.359 and 2.781 for (14,17) degrees of freedom for the two-tailed test.

(C) So, <u><em>the test statistics</em></u>  =  \frac{11,596^{2}  }{14,837^{2} } \times 1  ~  F__1_4,_ 1_7

                                     =  0.611

The value of the F-test statistic is 0.611.

Now, as we can see that our test statistics lie within the range of critical values of F, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region.

(D) Therefore, we conclude that there is no significant difference in the variances of the amounts spent in the two counties.

You might be interested in
An international company has 25,800 employees in one country. If this represents 31.1% of the companies employees, how many empl
aksik [14]

Answer:

Rounded to the nearest integer, the company has a total of 82,958 employees.

Step-by-step explanation:

Given that an international company has 25,800 employees in one country, if this represents 31.1% of the companies employees, to determine how many employees does it have in total, the following calculation must be performed:

31.1 = 25,800

100 = X

100 x 25,800 / 31.1 = X

2,580,000 / 31.1 = X

82,958.1 = X

Thus, rounded to the nearest integer, the company has a total of 82,958 employees.

3 0
3 years ago
Solve for X (picture included)
Fynjy0 [20]

Answer:

x = 41

Step-by-step explanation:

(2x+20) + (2x-4) = 180 degrees

4x+16 = 180 degrees

4x = 164

x = 41

The two sides are supplementary and add up to 180 degrees.

6 0
3 years ago
I NEED HELP PLSS ASAP
Katena32 [7]

Answer:

I don't know why this always happens to me it looks black can u ask the question and I will answer

6 0
3 years ago
Divide mentally<br> 270 divide 3=
yanalaym [24]

27/3 = 9 so 270/3 = 90

4 0
3 years ago
Read 2 more answers
Help please it’s a text
nikitadnepr [17]

Answer:

D

please mark brainlist!!! please

4 0
3 years ago
Read 2 more answers
Other questions:
  • QUICKLY !!
    5·1 answer
  • When should you use the fact that (a+b)4=a4+4a3b+6a2b2+4ab3+b4 answers?
    9·1 answer
  • A bracelet that normally sells for $30.00 is on sale for $25.50. What is the percent discount?
    5·1 answer
  • 6x + 1 = 2(3x - 2) + 5 A) x = 0 B) x = 12 C) x = 1 12 D) infinitely many solutions
    6·2 answers
  • The graph of the function f(x) = (x - 3)(x + 1) is shown.
    8·2 answers
  • What type of expense is a toll
    9·2 answers
  • How do you find the slope when you are only given an equation or a table?
    15·2 answers
  • CU,
    12·1 answer
  • Help im giving brainliest to the person who helps me with both questions! :)
    14·1 answer
  • Calculate the number in the middle of -7 and 6
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!