An economist is interested in studying the income of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the width of the 90% confidence interval

The width is  

Step-by-step explanation:

From the question we are told that

  The sample size is n =  50

  The  population standard deviation is  

   The sample size is  

Given that the confidence level is  90%  then the level of significance can be mathematically represented as

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

Generally the margin of error is mathematically represented as

substituting values

=>                

  The width of the 90%  confidence level is mathematically represented as

substituting values

your answer would be 10x - 1

let f (x ) is a function and c be a positive real number,   the graph of the function g (x ) = f (cx ) is represented as follows.

when, c > 1,   the function compresses it in the x - direction.

when, 0 < c < 1, the function stretches it.

the function is g ( x ) = (9x )2.

the heighest power of x in g ( x ) = (9x )2 is 2, so the parent function is square function.

the equation of parent function is f ( x ) = x 2 .

the function is g ( x ) = (9x )2 and the parent function is f ( x ) = x 2 .

so, the functions f and g have the following relationship.

g ( x ) = f ( 9x ).

compare the function g ( x ) = f ( 9x ) with g (x ) = f (cx ).

c = 9 ( > 1 ).

so, the function g (x ) = (9x )2 compresses it in the x - direction.

step-by-step explanation: