It has been reported that 20.4% of incoming freshmen indicate that they will major in business or a related field. A random sample of 400 incoming college freshmen was asked their preference, and 95 replied that they were considering business as a major. Estimate the true proportion of freshman business majors with 98% confidence. Does your interval contain 20.4%?

The  98% confidence interval

The confidence interval contains  20.4%

Step-by-step explanation:

From the question we are told that

    The sample size is  n =  400

The number that replied that they were considering business as a major

  The  sample proportion is mathematically  evaluated as

Given that the confidence level 98% then the level of significance is evaluated as

Next we obtain the critical value of  from the normal distribution table is  

  Generally the margin of error is mathematically represented as

The  98%  confidence interval is mathematically represented

 =>    

=>      

an advantage of the standard deviation is that it increases as the dispersion of the data increases. e. the interquartile range is preferred when the data are not skewed or no have outliers. an advantage of the standard deviation is that it uses all the observations in its computation.