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
juin [17]
3 years ago
15

With double-digit annual percentage increases in the cost of health insurance, more and more workers are likely to lack health i

nsurance coverage (USA Today, January 23, 2004). The following sample data provide a comparison of workers with and without health insurance coverage for small, medium, and large companies. For the purposes of this study, small companies are companies that have fewer than 100 employees. Medium companies have 100 to 999 employees, and large companies have 1000 or more employees. Sample data are reported for 50 employees of small companies, 75 employees of medium companies, and 100 employees of large companies.
Health Insurance
Size of Company Yes No Total
Small 33 17 50
Medium 68 7 75
Large 88 12 100
Conduct a test of independence to determine whether employee health insurance coverage is independent of the size of the company. Use = .05.
1. Compute the value of the 2 test statistic (to 2 decimals).
2. The p value is :_____.
a. less than .005
b. between .005 and .01
c. between .01 and .025
d. between .025 and .05
e. between .05 and .10
f. greater than .10
3. What is your conclusion?
a. health insurance coverage is not independent of the size of the company
b. Cannot reject the assumption that health insurance coverage and size of the company are independent
4. The USA Today article indicated employees of small companies are more likely to lack health insurance coverage. Calculate the percentages of employees without health insurance based on company size (to the nearest whole number).
Small %
Medium %
Large %
Mathematics
1 answer:
Dahasolnce [82]3 years ago
3 0

Answer:

1.  χ² = <u>  15.3902 </u>

2. The p value is :_____.a. less than .005

3.  Conclusion

a. health insurance coverage is not independent of the size of the company

4. The percentages of employees

Small %=   33/50= 0.66

Medium %= 68/75 = 0.91

Large %= 88/100= 0.88

Step-by-step explanation:

1) We set up our null and alternative hypothesis as

H0: the employee health insurance coverage is independent of the size of the company

against the claim

Ha: the employee health insurance coverage is not independent of the size of the company

2) the significance level alpha is set at 0.05

3) the test statistic under H0 is

χ²= ∑ (O - E)²/ E where O is the observed and E is the expected frequency

which has an approximate chi square distribution with ( 3-1) (2-1)=  2 d.f

4) Computations:

Under H0 , the observed frequencies are :

Observed       Expected E        (O-E)         (O-E)²             (O-E)²/E

33                   42                      -9               81                    1.928  

68                  63                         5              25                  0.3968

88                  84                         4               16                  0.1904

17                    8                           9              81                  10.125

7                     12                          -5             21                    1.75

<u>12                    16                         -4              16                     1              </u>

<u>                                                                                           15.3902    </u>

Expected Values are calculated using the formula :

Row Total * Column Total / sample size

E1= (33+17) (33+ 68+88)/ 50+75+100= 42

E4= (33+17) (17+ 7+ 12)/ 50+75+100=8

E2= (68+7) (33+ 68+88)/ 50+75+100= 63

E5= (68+7)  (17+ 7+ 12)/ 50+75+100= 12

E3= (88+12) (33+ 68+88)/ 50+75+100= 84

E6= (88+12)  (17+ 7+ 12)/ 50+75+100= 16

5) The critical region is χ² ≥ χ² (0.05)2 = 5.99

6) Conclusion:

The calculated χ² = <u>  15.3902    </u>falls in the critical region χ² ≥  5.99  so we reject the null hypothesis that the employee health insurance coverage is NOT independent of the size of the company.

2. The p value is :_____.

a. less than .005

The p-value is .000385.

3.  Conclusion

a. health insurance coverage is not independent of the size of the company

4. The percentages of employees

Small %=   33/50= 0.66

Medium %= 68/75 = 0.91

Large %= 88/100= 0.88

You might be interested in
3
Karolina [17]
Oh okie so I Pepeooooo oit the way
4 0
2 years ago
Solve this problem please<br>​
zhannawk [14.2K]

Answer:

Check pdf

Step-by-step explanation:

Download pdf
3 0
3 years ago
Determine the Value of x,y and z.
Aleksandr-060686 [28]

Answer:

x=9

y=16

z=12

Step-by-step explanation:

7 0
3 years ago
3.<br> If r=9.b=5, and g=-6, what does (r +b-8)(b + g) equal?
VLD [36.1K]

Answer:

-6

Step-by-step explanation:

r = 9, b = 5, g = -6

Plug these values into (r + b - 8)(b + g)

[(9) + (5) - 8]*[(5) + (-6)]

Combine like terms in the brackets

[6]*[-1]

6 times -1 equals -6, so that is your answer

8 0
3 years ago
Please this is a test I need to show work to so please explain
Ratling [72]
Explain what? where’s the question dude
7 0
3 years ago
Other questions:
  • Balsamic vinegar <br><br> Amount: 1 cup<br><br> Unit cost: $12.70/quart<br><br> Total cost =
    14·2 answers
  • Seven more than the cube of a number is what
    13·1 answer
  • A single person pays $4,500 in income taxes on a gross income of $30,000. How much would a single person be expected to pay if h
    7·2 answers
  • A deposit of $5,000 is made into a savings account which earns 3 3 4 % interest compounded annually. If no additional deposits o
    12·2 answers
  • Which term is a term in this expression?<br> -3x-7(x+4)
    6·1 answer
  • Keisha rolls two 6-sided number cubes. What is the probability that she will roll a number less than 7? (Leave your answer as a
    13·1 answer
  • Could you possibly figure this out for me​
    12·1 answer
  • Dante wants to buy a new sound system for his room. He borrows $500 from his older sister and agrees to pay her 6% simple annual
    14·2 answers
  • Can someone solve 6 and 7 for me I will mark you the brainly pls help I will really appreciate
    15·1 answer
  • GUY PLEASE HELP ME FAST, NO LINK PLS. QUESTION IS DUE ASAP
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!