Question

State H0 and H1. Answer the question. Use megastat and submit software output.

See Worksheet 4. 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 53% of all physician visits were to primary care physicians, 19% to medical specialists, 17% to surgical specialists, and 11% to emergency departments. Test at the .01 significance level if Isaac employees differ significantly from the national survey distribution.

National	Problem 6
Proportion	Visit Type	Observed	Expected
0.53	Primary care	29
0.19	Medical specialist	11
0.17	Surgical specialist	16
0.11	Emergency	4
		60

Answer 1

Hypotheses are:

H0: Isaac employees do not differ significantly from the national survey distribution.

Ha: Isaac employees differ significantly from the national survey distribution.

To use megastat first we need to calculate the expected freqeuncies. Since sum of observed frequencies is 60 so expected frequency will be 60 * proportion.

Following table shows calcualtions:

Proprotion, p	Observed , O	Expected , E=60*p
0.53	29	31.8
0.19	11	11.4
0.17	16	10.2
0.11	4	6.6
Total	60	60

Following is the screen shot of excel to run chi square goodness of fit test:

Following is the output generated by excel:

Goodness of Fit Test
	observed	expected	O - E	(O - E)² / E	% of chisq
	29	31.800	-2.800	0.247	5.38
	11	11.400	-0.400	0.014	0.31
	16	10.200	5.800	3.298	71.96
	4	6.600	-2.600	1.024	22.35
	60	60.000	0.000	4.583	100.00
	4.58	chi-square
	3	df
	.2050	p-value

The p-value is: 0.2050

Since p-value is greater than 0.01 so we fail to reject the null hypothesis.

That is we cannot conclude that Isaac employees differ significantly from the national survey distribution.