A professor teaches an undergraduate course in statistics. He uses a lot of sports examples to explain key concepts. He is concerned that this may have biased his instruction to favor male students. To test this, he measures exam grades among women (n = 10) and men (n = 10). The mean score in the male group was 82 ± 4.0 (M ± SD); in the female group, it was 74 ± 8.0 (M ± SD) points. If the null hypothesis is that there is no difference in exam scores, then test the null hypothesis at a .05 level of significance for a two-tailed test. Use denominator of 2.98.

The null hypothesis is  rejected

Therefore there is sufficient evidence to conclude that the professors teaching method favored the male

Step-by-step explanation:

From the question we are told that

   The sample size for each population is  

   The  first sample  mean is  

    The  second sample  mean is  

    The  first standard deviation is  

    The second standard deviation is  

     The  level of significance is  

The  null hypothesis is  

The  alternative  hypothesis is  

Generally the standard error is mathematically represented as

=>        

=>        

Generally the test statistics is mathematically represented as

=>        

=>        t =  2.83

Generally the p-value  mathematically represented as

From the z table  

So

Since  

Hence the null hypothesis is  rejected

Therefore there is sufficient evidence to conclude that the professors teaching method favored the male

d

step-by-step explanation:

by observation, we can see that the the graph is simply the graph of y = |x| that has been shifted 4 units downwards and 3 units to the left.

we can recognize in choice d :

y = | x + 3 |   - 4 (rewriting in general form)

y = | x - (- 3) |   - 4

the "-4 " term means   that the graph has been shifted by 4 units in the negative y direction

the "-3 " term means   that the graph has been shifted by 3 units in the negative x direction

this matches our observation of the graph described above.

x = -3

y = -18

step-by-step explanation:

to solve by substitution, substitute one variable and solve for the other. then substitute again to find the remaining variable.

x-1/3(3x-9) = -3 since y=3x-9 substittute y.

x-1/3(3x-9)=-3

x + x +3 = -3

2x+3=-3

2x+3-3= -3-3

2x=-6

x=-3

substitute again into y=3x-9

y=3(-3)-9

y=-9-9

y=-18