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Categorical Data.pdf - Inference of Categorical Data On...

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Inference of Categorical Data: On your own 1. Is there convincing evidence that Spain has seen a change in its atheism index between 2005 and 2012? > spain2005 <- atheism %>% + filter(nationality == "Spain" & year == 2005) > inference(y = spain2005$response, est = "proportion", type = "ci", + method = "theoretical", success = "atheist") Single proportion -- success: atheist Summary statistics: p_hat = 0.1003 ; n = 1146 Check conditions: number of successes = 115 ; number of failures = 1031 Standard error = 0.0089 95 % Confidence interval = ( 0.083 , 0.1177 ) > spain2012 <- atheism %>% + filter(nationality == "Spain" & year == 2012) > inference(y = spain2012$response, est = "proportion", type = "ci", + method = "theoretical", success = "atheist") Single proportion -- success: atheist Summary statistics: p_hat = 0.09 ; n = 1145
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Check conditions: number of successes = 103 ; number of failures = 1042 Standard error = 0.0085 95 % Confidence interval = ( 0.0734 , 0.1065 ) The 95% confidence interval for 2005 is ( 0.083 , 0.1177 ) and for 2012 is ( 0.0734 , 0.1065 ), which is not significantly different. Majority of the CI still overalap. Hence, we do not have enough evidence that there has been a change in Spain s atheism index between 2005 and 2012.
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