Question

6.36 Diabetes and unemployment: A 2012 Gallup poll surveyed Americans about their employment status and whether or not they have diabetes. The survey results indicate that 1.5% of the 47,774 employed (full or part time) and 2.5% of the 5,855 unemployed 18-29 year olds have diabetes.


(a) Create a two-way table presenting the results of this study.

	Diabetes	No Diabetes
Employed
Unemployed

(b) State appropriate hypotheses to test for independence of incidence of diabetes and employment status.

• H₀: μ_diabetes=μ_employed
  H_a: μ_diabetes ≠ μ_employed
• H₀: Diabetes status and employment status are independent
  H_a: Diabetes status and employment status are not independent
• H₀: Diabetes status and employment status are dependent
  H_a: Diabetes status and employment status are not dependent

(c) The sample difference is about 1%. If we completed the hypothesis test, we would find that the p-value is very small (about 0), meaning the difference is statistically significant. Use this result to explain the difference between statistically significant and practically significant findings.

• Being unemployed causes people to get diabetes at a higher rate
• If our data don't provide strong enough evidence to reject the null hypothesis we should just collect more data until we can report the results that we want
• Since the sample sizes are so large and the difference between the two sample proportions is so small, we observe a statistically significant difference which may not be practically significant

Answer 1

(a) The table is given below.

	Diabetes	No Diabetes
Employed	717	47057
Unemployed	146	5709

(The values can also be 716, 47058, 147, 5708.)

(b) H₀: Diabetes status and employment status are independent.
H_a: Diabetes status and employment status are not independent.

(c) Since the p-value is very small, we reject the null hypothesis. Our answer is -> Since the sample sizes are so large and the difference between the two sample proportions is so small, we observe a statistically significant difference which may not be practically significant.