A Biology teacher wants to see if there is any difference in the abilities of students enrolled in biology today and those enrolled five years ago. A sample of final examination scores from students enrolled today and from students enrolled five years ago was taken. You are given the following information. Today Five Years Ago 81 85 σ 14.5 8.5 n 81 36 ​ The point estimate for the difference between the means of the two populations is

The point estimate for the difference between the means of the two populations is x1`-x2`= 81-85=-4 where x1` is the mean of the of the first population and x2` is the mean of the second population.

Step-by-step explanation:

The data given is

               Today               Five Years Ago

X`                 81                           85

σ              14.5                        8.5

n                81                          36

The point estimate for the difference between the means of the two populations is x1`-x2`= 81-85=-4 where x1` is the mean of the of the first population and x2` is the mean of the second population.

The test statistics that will be used is

Z= x1-x2/ √σ₁²/ n₁ + σ₂²/n₂

Z=  81- 85/ √14.5² /81 + 8.5² /36

z= -4/√210.25/81+ 72.25/36

z= -4/2.1454

z= -1.8644

need more detail

step-by-step explanation:

lele

the answer is a) y= 2 csc [0.5 (x+pi/2)]-1

step-by-step explanation: