An experiment was conducted to assess the efficacy of spraying oats with malathion tocontrol the cereal leaf beetle. A sample of 10 farms were selected at random and eachfarm was assigned at random to either the control group (no spray) or the treatmentgroup (spray). At the conclusion of the experiment, a plot on each farm was selected andthe number of larvae per stem was measured. The powerof the test refers to:

a. the ability to detect an effect of malathion when in fact there is no effect.
b. the ability to not detect an effect of malathion when in fact there is no effect.
c. the ability to detect an effect of malathion when in fact there is an effect.
d. the ability to make a correct decision regardless if malathion had an effect or not.
e. failing to detect an effect of malathion when in fact there is an effect.

C

Step-by-step explanation:

Solution:-

- An experiment on the efficacy of spraying malathion on oats to control the growth cereal leaf beetle.

- A sample of n = 10 farms was taken at random. Each farm was either subjected to control group ( no spray ) or the treatment group ( spray ).

- Power ( β ) is the probability of rejecting the null hypothesis when, in fact, it is false. I.e the test statistics lie in the rejection region or the benefit of adding malathion is proven in-effective when in fact it is in-effective.

- Power is the probability of avoiding a ( Type II error ). Mathematically expressed as:

                    Type II Error = 1 - β

- Power is the probability of making a correct decision (to reject the null hypothesis) when the null hypothesis is false.

- The probability that a test of significance will pick up on an effect that is present.

Hence,

It is the ability to detect the effectiveness of malathion when in fact it is effective.

what are you trying to solve here

step-by-step explanation:

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.