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.
(b) State appropriate hypotheses to test for independence of incidence of diabetes and employment status.
(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.
(a) The table is given below.
(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.
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