John Isaac Inc a designer and installer of industrial signs

John Isaac Inc., a designer and installer of industrial signs, employs 60 people. The company recorded the type of the most recent visit to a doctor by each employee. A national assessment conducted in 2014 found that 43% of all physician visits were to primary care physicians, 24% to medical specialists, 24% to surgical specialists and 9% to emergency departments. Test at the 0.02 significance level if Isaac employees differ significantly from the survey distribution.

Here are their results:

Visit Type Number of Visits

Primary care            32

Medical specialist 8

Surgical specialist    14

Emergency         6

State the decision rule. Use 0.02 significance level. (Round your answers to 3 decimal places.)

H0: The employee visits do not differ from the survey distribution.

H1: The employee visits differ from the survey distribution. Reject H0 if X^2 >

Compute the value of chi-square. (Round your answer to 2 decimal places.)

X^2 =

What is your decision regarding H0?   REJECT/DO NOT REJECT H0 .

Isaac employees DIFFER/DO NOT DIFFER significantly from the survey distribution.

Solution

John Isaac Inc., a designer and installer of industrial signs, employs 60 people. The company recorded the type of the most recent visit to a doctor by each employee. A national assessment conducted in 2014 found that 43% of all physician visits were to primary care physicians, 24% to medical specialists, 24% to surgical specialists and 9% to emergency departments. Test at the 0.02 significance level if Isaac employees differ significantly from the survey distribution.

Here are their results:

Visit Type Number of Visits

Primary care            32

Medical specialist 8

Surgical specialist    14

Emergency         6

State the decision rule. Use 0.02 significance level. (Round your answers to 3 decimal places.)

Table value at 0.02 level =9.837

If the calculated test value > 9.837, reject the null hypothesis.

Reject H0 if X^2 > 9.837

H0: The employee visits do not differ from the survey distribution.

H1: The employee visits differ from the survey distribution. Reject H0 if X^2 >

Compute the value of chi-square.

Goodness of Fit Test

observed

expected

O - E

(O - E)² / E

32

25.800

6.200

1.490

8

14.400

-6.400

2.844

14

14.400

-0.400

0.011

6

5.400

0.600

0.067

60

60.000

0.000

4.412

4.41

chi-square

3

df

.2203

p-value

(Round your answer to 2 decimal places.)

X^2 = 4.41

What is your decision regarding H0?

DO NOT REJECT H0 .

Isaac employees DO NOT DIFFER significantly from the survey distribution.

Goodness of Fit Test
	observed	expected	O - E	(O - E)² / E
	32	25.800	6.200	1.490
	8	14.400	-6.400	2.844
	14	14.400	-0.400	0.011
	6	5.400	0.600	0.067
	60	60.000	0.000	4.412
	4.41	chi-square
	3	df
	.2203	p-value