A 90% confidence interval for the true proportion of voters who support the candidate is 0.45 to 0.53, which means that there is a 90% probability that the interval 0.45 to 0.53 contains the true proportion of voters who support the candidate.
Therefore, the following claims are justified:
e. A political reporter claims that at least 45% of registered voters favor this candidate. (This claim is supported by the lower bound of the confidence interval.)
The following claims are not justified:
a. A political reporter claims that 90% of registered voters favor this candidate. (This is not a correct interpretation of the confidence interval, which only provides a range of likely values for the true proportion of voters who support the candidate, not the exact value.)
c. A political reporter claims that at least 53% of registered voters favor this candidate. (This claim goes beyond the information provided by the upper bound of the confidence interval, which only indicates that there is a 90% probability that the true proportion of voters who support the candidate is less than or equal to 0.53.)
d. A political reporter claims that the majority of registered voters favor this candidate. (This claim goes beyond the information provided by the confidence interval, which does not indicate whether the majority of voters support the candidate or not. A majority is defined as more than 50%, so further analysis would be required to determine whether the majority of registered voters support the candidate or not.)