Presentation - Inference for Categorical data

6.21 National Health Plan

6.21 National Health Plan, Part III. Exercise 6.11 presents the results of a poll evaluating support for a generically branded “National Health Plan” in the United States. 79% of 347 Democrats and 55% of 617 Independents support a National Health Plan.

1. Calculate a 95% confidence interval for the difference between the proportion of Democrats and Independents who support a National Health Plan (p_D − p_I ), and interpret it in this context. We have already checked conditions for you.

nD <- 347
nI<- 617
pD <- 0.79
pI <- 0.55

# Point estimate = pD - pI
PE <- pD -pI

# SE <- sqrt((p * (1-p))/n)

SE <- sqrt(((pD * (1-pD))/nD) + ((pI * (1-pI))/nI))

#Z score for 95% CI = 1.96

#ME for 95% CI = 1.96*SE

ME <- 1.96 * SE

lower <- PE-ME
upper <- PE+ME

lower

## [1] 0.1818824

upper

## [1] 0.2981176

2. True or false: If we had picked a random Democrat and a random Independent at the time of this poll, it is more likely that the Democrat would support the National Health Plan than the Independent.

TRUE : We see the confidence interval range is (0.1818824, 0.2981176) which doesn’t include 0 so it is more likely that Democrat would support the National health plan than the Independent