Comparing two population proportions (independent samples) Aa Aa a Most major survey research organizations do not include wireless telephone...

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4. Comparing two population proportions (independent samples) Aa Aa a Most major survey research organizations do not include wireless telephone numbers when conductingrandom-digit-dial telephone surveys. If there are differences between persons with and without landline phones,using a random-digit-dial telephone survey may introduce bias into the survey results. Data on a broad range of health topics are collected through personal household interviews of a representativesample of the US. civilian noninstitutionalized population in the National Health Interview Survey (NHIS). Sincerespondents are also asked about their telephones, the NHIS data allow you to compare the health status of personswith and without landline phones. Let p1 denote the proportion of adults living in wireless phone—only homes who are diabetic and p2 denote theproportion of adults living in landline phone homes who are diabetic. Independent random samples are selected fromthe two populations. Sample 1, with sample size n1 = 272, provides a sample proportion pix 0.05. Sample 2, withsample size n2 = 400, provides a sample proportion [32% 0.09. (The sample results are representative of the datacollected in the NHIS, but the sample sizes are much smaller.) Use the Distributions tool to help you answer the questions that follow.