Question

# 6.36 Diabetes and unemployment: A 2012 Gallup poll surveyed Americans about their employment status and whether...

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: μdiabetesemployed
Ha: μdiabetes ≠ μemployed
• H0: Diabetes status and employment status are independent
Ha: Diabetes status and employment status are not independent
• H0: Diabetes status and employment status are dependent
Ha: 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

(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.
Ha: 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.

#### Earn Coins

Coins can be redeemed for fabulous gifts.