Which of the following is not true when dealing with independent samples? choose the correct answer below.
a. the confidence interval estimate of µ 1-µ 2 is ( x 1 - x 2 ) - e < ( µ 1 - µ 2 ) < ( x 1 - x 2 ) + e.
b. when making an inference about the two means, the p-value and traditional methods of hypothesis testing result in the same conclusion as the confidence interval method.
c. the variance of the differences between two independent random variables equals the variance of the first random variable - the variance of the second random variable.
d. the null hypothesis µ 1=µ 2 or µ 1 - µ 2 = 0 can be tested using the p-value method, the traditional method, or by determining if the confidence interval limits for µ 1-µ 2 contain 0.

Step-by-step explanation:

Give that hypothesis testing is done using independent samples.

A) The confidence interval estimate of µ 1-µ 2 is ( x 1 - x 2 ) - E < ( µ 1 - µ 2 ) < ( x 1 - x 2 ) + E.

This is true.  because margin of error is subtracted and added to get lower/upper bounds.

B) When making an inference about the two means, the P-value and traditional methods of hypothesis testing result in the same conclusion as the confidence interval method. True

C) False  because Var(X-Y) = Var(x)+Var(Y) when independent

D) True.  

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this