. A 2003 Harris Poll of 993 randomly selected American adults found that 69% believed in
capital punishment (death penalty). A sample size of 1010 American adults in 2000 found
that 64% believed in capital punishment. Write the hypotheses for a significance test to
determine whether a significantly higher proportion of American adults believed in capital
punishment in 2003 than in 2000.
To write the hypotheses for the significance test, we need to define the null hypothesis (H0) and the alternative hypothesis (Ha).
Null hypothesis (H0): The proportion of American adults who believed in capital punishment in 2003 is the same as in 2000.
Alternative hypothesis (Ha): The proportion of American adults who believed in capital punishment in 2003 is significantly higher than in 2000.
Symbolically, we can represent these hypotheses as follows:
H0: p2003 = p2000
Ha: p2003 > p2000
In these hypotheses, p2003 represents the proportion of American adults who believed in capital punishment in 2003, and p2000 represents the proportion of American adults who believed in capital punishment in 2000.
To determine if the proportion of believers in capital punishment significantly increased from 2000 to 2003, we will conduct a one-tailed test of proportions with the alternative hypothesis stating that the proportion in 2003 is higher.