Answer:
We are confident at 99% that the difference between the two proportions is between  
Step-by-step explanation:
Part a
Data given and notation  
 represent the number people registered as Democrats
 represent the number people registered as Democrats
 represent the number of people registered as Republicans
 represent the number of people registered as Republicans
 sampleselcted
 sampleselcted
 represent the proportion of people registered as Democrats
 represent the proportion of people registered as Democrats
 represent the proportion of people registered as Republicans
 represent the proportion of people registered as Republicans
The standard error is given by this formula:

And the standard error estimated given by the problem is 0.008
Part b
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".  
The margin of error is the range of values below and above the sample statistic in a confidence interval.  
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".  
 represent the real population proportion of Democrats that approve of the way the California Legislature is handling its job
 represent the real population proportion of Democrats that approve of the way the California Legislature is handling its job  
 represent the estimated proportion of Democrats that approve of the way the California Legislature is handling its job
 represent the estimated proportion of Democrats that approve of the way the California Legislature is handling its job  
 is the sample size for Democrats
 is the sample size for Democrats 
 represent the real population proportion of Republicans that approve of the way the California Legislature is handling its job
 represent the real population proportion of Republicans that approve of the way the California Legislature is handling its job  
 represent the estimated proportion of Republicans that approve of the way the California Legislature is handling its job
 represent the estimated proportion of Republicans that approve of the way the California Legislature is handling its job 
 is the sample for Republicans
 is the sample for Republicans 
 represent the critical value for the margin of error
 represent the critical value for the margin of error  
The population proportion have the following distribution  
 
  
The confidence interval for the difference of two proportions would be given by this formula  
 
  
For the 90% confidence interval the value of  and
 and  , with that value we can find the quantile required for the interval in the normal standard distribution.
, with that value we can find the quantile required for the interval in the normal standard distribution.  
 
  
And replacing into the confidence interval formula we got:  
 
  
 
  
And the 99% confidence interval would be given (0.380;0.420).  
We are confident at 99% that the difference between the two proportions is between 