A random sample of 1800 adult women indicated that 841 of them asked for medical assistance last time they felt sick. The same sized sample of men indicated that 793 of them asked for medical assistance. Use the z-values rounded to three decimal places to obtain the answers. a) Construct a 98% confidence interval for the difference in the two tests. Round your answers to five decimal places (e. g. 98.76543).

And the 98% confidence interval would be given (-0.0127;0.0647).  

We are confident at 98% that the difference between the two proportions is between

Step-by-step explanation:

Previous concepts

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".  

Solution to the problem

represent the real population proportion for women

represent the estimated proportion for women

is the sample size required for women

represent the real population proportion for men

represent the estimated proportion for men

is the sample size required for Brand B

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 98% confidence interval the value of and , 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 98% confidence interval would be given (-0.0127;0.0647).  

We are confident at 98% that the difference between the two proportions is between

b.an increase in a causes b to decrease